{ "cells": [ { "cell_type": "markdown", "id": "98f649b7", "metadata": {}, "source": [ "# Solving Systems of IVPs\n", "\n", "## Overview, Objectives, and Key Terms\n", "\n", "The last lesson focused on one first-order initial-value problem at a time. Many useful models do not arrive that politely. A second-order spring equation, a set of coupled nuclide balances, and a spatial discretization of an ADR model all produce several unknowns that evolve together.\n", "\n", "The move is simple: collect the unknowns into a state vector and solve one vector IVP.\n", "\n", "By the end of this lesson, you should be able to\n", "\n", "- rewrite a higher-order ODE or coupled balance as a first-order system,\n", "- use forward and backward Euler on a linear system $\\mathbf{y}'=\\mathbf{A}\\mathbf{y}+\\mathbf{s}$,\n", "- call `scipy.integrate.solve_ivp` for a system using the signature `f(t, y, ...)`, and\n", "- check state ordering, output shapes, and active time scales.\n", "\n", "**Key terms:** state vector, first-order system, forward Euler, backward Euler, stiffness, `solve_ivp`, `t_eval`.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "706d1f3b", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:48.503044Z", "iopub.status.busy": "2026-07-08T03:49:48.502944Z", "iopub.status.idle": "2026-07-08T03:49:48.997352Z", "shell.execute_reply": "2026-07-08T03:49:48.996875Z" } }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import solve_ivp\n", "\n", "PURPLE = \"#512888\"\n", "ORANGE = \"#D55E00\"\n", "BLUE = \"#2563EB\"\n", "GREEN = \"#059669\"\n", "RED = \"#DC2626\"\n", "INK = \"#1F2937\"\n", "MUTED = \"#64748B\"\n", "GRID = \"#E5E7EB\"\n", "PANEL = \"#F5F6F8\"\n", "\n", "plt.rcParams.update({\n", " \"figure.figsize\": (7.2, 4.2),\n", " \"axes.edgecolor\": INK,\n", " \"axes.labelcolor\": INK,\n", " \"xtick.color\": INK,\n", " \"ytick.color\": INK,\n", " \"grid.color\": GRID,\n", "})\n" ] }, { "cell_type": "markdown", "id": "56a2eaef", "metadata": {}, "source": [ "## A System Is One IVP With More Bookkeeping\n", "\n", "A scalar IVP has the form\n", "\n", "$$\n", "\\frac{dy}{dt}=f(t,y), \\qquad y(t_0)=y_0.\n", "$$\n", "\n", "A system has the same structure, except the unknown is a vector:\n", "\n", "$$\n", "\\frac{d\\mathbf{y}}{dt}=\\mathbf{f}(t,\\mathbf{y}), \\qquad \\mathbf{y}(t_0)=\\mathbf{y}_0.\n", "$$\n", "\n", "This is exactly the same bookkeeping idea we used for finite-volume balances: decide what is being counted, put those quantities in a vector, and write a balance for each entry.\n", "\n", "For a linear system, the right-hand side often looks like\n", "\n", "$$\n", "\\mathbf{y}' = \\mathbf{A}\\mathbf{y} + \\mathbf{s}(t),\n", "$$\n", "\n", "where $\\mathbf{A}$ contains the coupling between unknowns and $\\mathbf{s}$ contains external sources.\n" ] }, { "cell_type": "markdown", "id": "74b15775", "metadata": {}, "source": [ "## From One Spring Equation to Two First-Order Equations\n", "\n", "Consider a damped spring-mass system:\n", "\n", "$$\n", " m \\frac{d^2 x}{dt^2} = -k x(t) - a \\frac{dx}{dt}.\n", "$$\n", "\n", "The model is second order because it contains $x''$. To use Euler's method or `solve_ivp`, we rewrite it as a first-order system. Define\n", "\n", "$$\n", " u = x', \\qquad u' = x''.\n", "$$\n", "\n", "Then\n", "\n", "$$\n", "\\frac{dx}{dt}=u,\n", "\\qquad\n", "\\frac{du}{dt}=\\frac{-kx-au}{m}.\n", "$$\n", "\n", "We will use the state ordering\n", "\n", "$$\n", "\\mathbf{y}=\\begin{bmatrix}x \\\\ u\\end{bmatrix},\n", "$$\n", "\n", "which matches the worksheet. With that ordering,\n", "\n", "$$\n", "\\mathbf{y}'=\n", "\\underbrace{\\begin{bmatrix}\n", "0 & 1 \\\\\n", "-k/m & -a/m\n", "\\end{bmatrix}}_{\\mathbf{A}}\n", "\\mathbf{y}.\n", "$$\n" ] }, { "cell_type": "code", "execution_count": null, "id": "717dd862", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:48.998716Z", "iopub.status.busy": "2026-07-08T03:49:48.998567Z", "iopub.status.idle": "2026-07-08T03:49:49.001547Z", "shell.execute_reply": "2026-07-08T03:49:49.001138Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input\n", "k=0.100, a=0.200, m=0.500\n", "y0 = [x0, u0] = [0. 1.]\n", "\n", "System matrix A:\n", "[[ 0. 1. ]\n", " [-0.2 -0.4]]\n" ] } ], "source": [ "# Input block: spring-mass parameters and state ordering.\n", "k = 0.1 # spring constant\n", "a = 0.2 # damping coefficient\n", "m = 0.5 # mass\n", "x0 = 0.0 # initial position\n", "u0 = 1.0 # initial velocity\n", "\n", "A = np.array([[0.0, 1.0],\n", " [-k/m, -a/m]])\n", "y0 = np.array([x0, u0])\n", "\n", "print(\"Input\")\n", "print(f\"k={k:.3f}, a={a:.3f}, m={m:.3f}\")\n", "print(f\"y0 = [x0, u0] = {y0}\")\n", "print(\"\\nSystem matrix A:\")\n", "print(A)\n" ] }, { "cell_type": "markdown", "id": "242848c1", "metadata": {}, "source": [ "The first row of $\\mathbf{A}$ says $x'=u$. The second row says the velocity changes because the spring pulls back on the displacement and the damper pulls back on the velocity.\n", "\n", "That row-level reading is worth keeping. A matrix row is not just algebra; it is a statement about how one state variable changes.\n" ] }, { "cell_type": "markdown", "id": "82e30378", "metadata": {}, "source": [ "## Euler Methods for a Linear System\n", "\n", "For a scalar IVP, forward Euler uses the right-hand side at the old state. The vector version does the same thing:\n", "\n", "$$\n", "\\mathbf{y}_{n+1}=\\mathbf{y}_n + \\Delta t\\,\\mathbf{f}(t_n,\\mathbf{y}_n).\n", "$$\n", "\n", "For the linear homogeneous system $\\mathbf{y}'=\\mathbf{A}\\mathbf{y}$,\n", "\n", "$$\n", "\\boxed{\\mathbf{y}_{n+1}=\\left(\\mathbf{I}+\\Delta t\\,\\mathbf{A}\\right)\\mathbf{y}_n.}\n", "$$\n", "\n", "Backward Euler evaluates the right-hand side at the new state:\n", "\n", "$$\n", "\\mathbf{y}_{n+1}=\\mathbf{y}_n + \\Delta t\\,\\mathbf{A}\\mathbf{y}_{n+1}.\n", "$$\n", "\n", "Move the unknown terms to the left:\n", "\n", "$$\n", "\\boxed{\\left(\\mathbf{I}-\\Delta t\\,\\mathbf{A}\\right)\\mathbf{y}_{n+1}=\\mathbf{y}_n.}\n", "$$\n", "\n", "That is the same lesson as our balance-law linear systems: reduce the step to algebra, then solve the algebra.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "3413d575", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.002412Z", "iopub.status.busy": "2026-07-08T03:49:49.002320Z", "iopub.status.idle": "2026-07-08T03:49:49.004779Z", "shell.execute_reply": "2026-07-08T03:49:49.004183Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output\n", "forward Euler y1 = [0.5 0.8]\n", "backward Euler y1 = [0.4 0.8]\n" ] } ], "source": [ "# One step of forward and backward Euler.\n", "Delta = 0.5\n", "I = np.eye(2)\n", "\n", "y1_fe = (I + Delta*A) @ y0\n", "y1_be = np.linalg.solve(I - Delta*A, y0)\n", "\n", "print(\"Output\")\n", "print(f\"forward Euler y1 = {y1_fe}\")\n", "print(f\"backward Euler y1 = {y1_be}\")\n" ] }, { "cell_type": "markdown", "id": "652b4216", "metadata": {}, "source": [ "Both methods are using the same model and the same time step. They differ in where they evaluate the slope. Forward Euler asks, “where would the old slope take me?” Backward Euler asks, “what new state is consistent with the new slope?”\n" ] }, { "cell_type": "code", "execution_count": null, "id": "1a69da1f", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.005776Z", "iopub.status.busy": "2026-07-08T03:49:49.005678Z", "iopub.status.idle": "2026-07-08T03:49:49.008858Z", "shell.execute_reply": "2026-07-08T03:49:49.008482Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output\n", "y_fe shape: (21, 2)\n", "y_be shape: (21, 2)\n", "last backward-Euler state [x, u]: [-0.11808235 -0.07281104]\n" ] } ], "source": [ "def forward_euler_linear(A, y0, t):\n", " \"\"\"Return states for y' = A y using forward Euler.\"\"\"\n", " y = np.zeros((len(t), len(y0)))\n", " y[0] = y0\n", " for n in range(len(t) - 1):\n", " dt = t[n + 1] - t[n]\n", " y[n + 1] = (np.eye(len(y0)) + dt*A) @ y[n]\n", " return y\n", "\n", "\n", "def backward_euler_linear(A, y0, t):\n", " \"\"\"Return states for y' = A y using backward Euler.\"\"\"\n", " y = np.zeros((len(t), len(y0)))\n", " y[0] = y0\n", " I = np.eye(len(y0))\n", " for n in range(len(t) - 1):\n", " dt = t[n + 1] - t[n]\n", " y[n + 1] = np.linalg.solve(I - dt*A, y[n])\n", " return y\n", "\n", "# Time grid and numerical solutions.\n", "t = np.linspace(0.0, 10.0, 21)\n", "y_fe = forward_euler_linear(A, y0, t)\n", "y_be = backward_euler_linear(A, y0, t)\n", "\n", "print(\"Output\")\n", "print(f\"y_fe shape: {y_fe.shape}\")\n", "print(f\"y_be shape: {y_be.shape}\")\n", "print(f\"last backward-Euler state [x, u]: {y_be[-1]}\")\n" ] }, { "cell_type": "markdown", "id": "53072bea", "metadata": {}, "source": [ "Our arrays are shaped `(number of times, number of states)`. Column 0 is position $x$ and column 1 is velocity $u$. This is the shape many of our own loops naturally produce.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "d0cc5da6", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.009614Z", "iopub.status.busy": "2026-07-08T03:49:49.009530Z", "iopub.status.idle": "2026-07-08T03:49:49.070314Z", "shell.execute_reply": "2026-07-08T03:49:49.069816Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(t, y_fe[:, 0], color=ORANGE, marker=\"o\", label=\"forward Euler: x\")\n", "ax.plot(t, y_be[:, 0], color=PURPLE, marker=\"s\", label=\"backward Euler: x\")\n", "ax.axhline(0.0, color=MUTED, lw=1)\n", "ax.set_xlabel(\"time\")\n", "ax.set_ylabel(\"position\")\n", "ax.set_title(\"Spring-mass position from two Euler updates\")\n", "ax.grid(True, alpha=0.8)\n", "ax.legend()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "829d54b2", "metadata": {}, "source": [ "## `solve_ivp`: The General-Purpose IVP Tool\n", "\n", "For routine work, use `scipy.integrate.solve_ivp`. It expects the right-hand side in the order\n", "\n", "```python\n", "def rhs(t, y, ...):\n", " return ...\n", "```\n", "\n", "This is an important detail. Older `odeint` examples often used `f(y, t, ...)`; `solve_ivp` uses `f(t, y, ...)`.\n", "\n", "The core call is\n", "\n", "```python\n", "sol = solve_ivp(rhs, t_span=(t0, tf), y0=y0, t_eval=t, args=(...))\n", "```\n", "\n", "where `t_eval` asks for output at the times we care about. Internally, the solver is free to take different steps.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "841019f9", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.071291Z", "iopub.status.busy": "2026-07-08T03:49:49.071197Z", "iopub.status.idle": "2026-07-08T03:49:49.077156Z", "shell.execute_reply": "2026-07-08T03:49:49.076634Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output\n", "success: True\n", "message: The solver successfully reached the end of the integration interval.\n", "sol.y shape: (2, 21) (states, times)\n", "transposed shape: (21, 2) (times, states)\n", "last solve_ivp state [x, u]: [-0.2560552 -0.03725 ]\n" ] } ], "source": [ "def spring_rhs(t, y, k, a, m):\n", " \"\"\"Right-hand side for y = [x, u].\"\"\"\n", " x, u = y\n", " return np.array([u, (-k*x - a*u)/m])\n", "\n", "sol = solve_ivp(\n", " spring_rhs,\n", " t_span=(t[0], t[-1]),\n", " y0=y0,\n", " t_eval=t,\n", " args=(k, a, m),\n", " rtol=1e-9,\n", " atol=1e-11,\n", ")\n", "\n", "y_solve_ivp = sol.y.T\n", "x_solve_ivp = y_solve_ivp[:, 0]\n", "u_solve_ivp = y_solve_ivp[:, 1]\n", "\n", "print(\"Output\")\n", "print(f\"success: {sol.success}\")\n", "print(f\"message: {sol.message}\")\n", "print(f\"sol.y shape: {sol.y.shape} (states, times)\")\n", "print(f\"transposed shape: {y_solve_ivp.shape} (times, states)\")\n", "print(f\"last solve_ivp state [x, u]: {y_solve_ivp[-1]}\")\n" ] }, { "cell_type": "markdown", "id": "426bb861", "metadata": {}, "source": [ "Notice the shape convention. `solve_ivp` returns `sol.y` with states along rows and times along columns. When we want the same shape as our Euler arrays, we use `sol.y.T`.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "2a3615f7", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.078113Z", "iopub.status.busy": "2026-07-08T03:49:49.078018Z", "iopub.status.idle": "2026-07-08T03:49:49.152906Z", "shell.execute_reply": "2026-07-08T03:49:49.152484Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.plot(t, y_be[:, 0], color=PURPLE, marker=\"s\", label=\"backward Euler: x\")\n", "ax.plot(t, x_solve_ivp, color=INK, lw=2.2, label=\"solve_ivp: x\")\n", "ax.plot(t, y_be[:, 1], color=ORANGE, marker=\"o\", label=\"backward Euler: u\")\n", "ax.plot(t, u_solve_ivp, color=BLUE, lw=2.2, label=\"solve_ivp: u\")\n", "ax.axhline(0.0, color=MUTED, lw=1)\n", "ax.set_xlabel(\"time\")\n", "ax.set_ylabel(\"state value\")\n", "ax.set_title(\"Backward Euler and solve_ivp solve the same system\")\n", "ax.grid(True, alpha=0.8)\n", "ax.legend(ncol=2)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": null, "id": "4208d785", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.153885Z", "iopub.status.busy": "2026-07-08T03:49:49.153767Z", "iopub.status.idle": "2026-07-08T03:49:49.156184Z", "shell.execute_reply": "2026-07-08T03:49:49.155789Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output/check\n", "max |x_BE - x_solve_ivp| = 1.5559e-01\n", "max |u_BE - u_solve_ivp| = 8.9837e-02\n", "first requested time: 0.0, last requested time: 10.0\n" ] } ], "source": [ "# Output/check block: compare backward Euler to solve_ivp on the same output grid.\n", "error = y_be - y_solve_ivp\n", "max_position_error = np.max(np.abs(error[:, 0]))\n", "max_velocity_error = np.max(np.abs(error[:, 1]))\n", "\n", "print(\"Output/check\")\n", "print(f\"max |x_BE - x_solve_ivp| = {max_position_error:.4e}\")\n", "print(f\"max |u_BE - u_solve_ivp| = {max_velocity_error:.4e}\")\n", "print(f\"first requested time: {sol.t[0]:.1f}, last requested time: {sol.t[-1]:.1f}\")\n" ] }, { "cell_type": "markdown", "id": "ccc550cf", "metadata": {}, "source": [ "The backward-Euler result is a valid numerical solution, but it uses a deliberately coarse time step. `solve_ivp` adjusts internal steps to meet error tolerances, then reports the solution at the requested `t_eval` times.\n", "\n", "That distinction is central: `t_eval` controls output times, not necessarily every internal step the solver takes.\n" ] }, { "cell_type": "markdown", "id": "f24cdd5d", "metadata": {}, "source": [ "## A Fast/Slow Balance System\n", "\n", "Systems become more interesting when different state variables evolve on different time scales. A simple linear production-decay chain is\n", "\n", "$$\n", "\\begin{aligned}\n", "\\frac{dn_1}{dt} &= q - \\lambda_1 n_1, \\\\\n", "\\frac{dn_2}{dt} &= \\lambda_1 n_1 - \\lambda_2 n_2.\n", "\\end{aligned}\n", "$$\n", "\n", "Here $n_1$ is produced directly, $n_1$ feeds $n_2$, and $n_2$ decays slowly. If $\\lambda_1$ is much larger than $\\lambda_2$, then the first component moves quickly while the second component drifts slowly.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "fccfc02c", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.157174Z", "iopub.status.busy": "2026-07-08T03:49:49.157076Z", "iopub.status.idle": "2026-07-08T03:49:49.159837Z", "shell.execute_reply": "2026-07-08T03:49:49.159218Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Input\n", "lambda1=10, lambda2=0.01, q=1\n", "A_chain =\n", "[[-10. 0. ]\n", " [ 10. -0.01]]\n", "source = [1. 0.]\n" ] } ], "source": [ "# Input block: a fast/slow linear balance system.\n", "lambda1 = 10.0\n", "lambda2 = 0.01\n", "q = 1.0\n", "z0 = np.array([0.0, 0.0])\n", "A_chain = np.array([[-lambda1, 0.0],\n", " [ lambda1, -lambda2]])\n", "s_chain = np.array([q, 0.0])\n", "t_chain = np.linspace(0.0, 500.0, 400)\n", "\n", "print(\"Input\")\n", "print(f\"lambda1={lambda1:g}, lambda2={lambda2:g}, q={q:g}\")\n", "print(\"A_chain =\")\n", "print(A_chain)\n", "print(f\"source = {s_chain}\")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "1b64b08a", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.160761Z", "iopub.status.busy": "2026-07-08T03:49:49.160671Z", "iopub.status.idle": "2026-07-08T03:49:49.220328Z", "shell.execute_reply": "2026-07-08T03:49:49.219518Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Output\n", "RK45 success=True, function calls=10778\n", "BDF success=True, function calls=478\n", "final BDF state [n1, n2] = [ 0.1 99.3255131]\n" ] } ], "source": [ "def chain_rhs(t, z, lambda1, lambda2, q):\n", " n1, n2 = z\n", " return np.array([q - lambda1*n1, lambda1*n1 - lambda2*n2])\n", "\n", "sol_rk = solve_ivp(\n", " chain_rhs,\n", " (t_chain[0], t_chain[-1]),\n", " z0,\n", " t_eval=t_chain,\n", " args=(lambda1, lambda2, q),\n", " rtol=1e-7,\n", " atol=1e-10,\n", " method=\"RK45\",\n", ")\n", "\n", "sol_bdf = solve_ivp(\n", " chain_rhs,\n", " (t_chain[0], t_chain[-1]),\n", " z0,\n", " t_eval=t_chain,\n", " args=(lambda1, lambda2, q),\n", " rtol=1e-7,\n", " atol=1e-10,\n", " method=\"BDF\",\n", ")\n", "\n", "print(\"Output\")\n", "print(f\"RK45 success={sol_rk.success}, function calls={sol_rk.nfev}\")\n", "print(f\"BDF success={sol_bdf.success}, function calls={sol_bdf.nfev}\")\n", "print(f\"final BDF state [n1, n2] = {sol_bdf.y[:, -1]}\")\n" ] }, { "cell_type": "code", "execution_count": null, "id": "ee2cfa58", "metadata": { "execution": { "iopub.execute_input": "2026-07-08T03:49:49.221408Z", "iopub.status.busy": "2026-07-08T03:49:49.221309Z", "iopub.status.idle": "2026-07-08T03:49:49.398784Z", "shell.execute_reply": "2026-07-08T03:49:49.398176Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(10.2, 3.9), constrained_layout=True)\n", "\n", "ax0.plot(sol_bdf.t, sol_bdf.y[0], color=PURPLE, label=\"$n_1$ fast\")\n", "ax0.plot(sol_bdf.t, sol_bdf.y[1], color=ORANGE, label=\"$n_2$ slow\")\n", "ax0.set_xlabel(\"time\")\n", "ax0.set_ylabel(\"inventory\")\n", "ax0.set_title(\"Both states\")\n", "ax0.grid(True, alpha=0.8)\n", "ax0.legend()\n", "\n", "ax1.plot(sol_bdf.t, sol_bdf.y[0], color=PURPLE, label=\"$n_1$\")\n", "ax1.set_xlim(0, 2.0)\n", "ax1.set_xlabel(\"time\")\n", "ax1.set_ylabel(\"inventory\")\n", "ax1.set_title(\"Fast transient detail\")\n", "ax1.grid(True, alpha=0.8)\n", "ax1.legend()\n", "\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "c4b9a15f", "metadata": {}, "source": [ "The first inventory reaches its near-steady value quickly. The second inventory changes on a much longer time scale. That spread in time scales is the practical warning sign for stiffness.\n", "\n", "`solve_ivp` lets us choose methods explicitly. `RK45` is a good default for many non-stiff problems. `BDF` is built for stiff systems. The point here is not to memorize method internals; it is to recognize when a model contains fast and slow balances in the same state vector.\n" ] }, { "cell_type": "markdown", "id": "f37d2432", "metadata": {}, "source": [ "## What To Check Every Time\n", "\n", "After solving a system IVP, check the bookkeeping before trusting the curve.\n", "\n", "1. **State order:** Is the vector really `[x, u]`, `[n1, n2]`, or whatever the model statement says?\n", "2. **Right-hand-side signature:** For `solve_ivp`, did you write `f(t, y, ...)`?\n", "3. **Array shape:** `sol.y` is `(number of states, number of output times)`. Transpose it when you want rows to correspond to times.\n", "4. **Solver status:** Is `sol.success` true, and does the message make sense?\n", "5. **Time scales and units:** Does the result move on the expected time scale, and do the signs match the balance?\n", "\n", "The computational pattern is short:\n", "\n", "```python\n", "def rhs(t, y, ...):\n", " ...\n", " return dydt\n", "\n", "sol = solve_ivp(rhs, (t0, tf), y0, t_eval=t, args=(...))\n", "y_by_time = sol.y.T\n", "```\n", "\n", "The engineering work is deciding what belongs in the state vector and what each row of the derivative means.\n" ] }, { "cell_type": "markdown", "id": "2de31580", "metadata": {}, "source": [ "## Further Reading\n", "\n", "- SciPy documentation for [`solve_ivp`](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html)\n", "- SciPy user guide section on [integrating ordinary differential equations](https://docs.scipy.org/doc/scipy/tutorial/integrate.html)\n", "- Previous lessons: finite-volume bookkeeping in L10, ADR balances in L26, symbolic IVP scaffolds in L27, and scalar Euler methods in L28.\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.13" } }, "nbformat": 4, "nbformat_minor": 5 }