.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "examples_gallery/advanced_pdes/solver_comparison.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_examples_gallery_advanced_pdes_solver_comparison.py: Solver comparison ================= This example shows how to set up solvers explicitly and how to extract diagnostic information. .. GENERATED FROM PYTHON SOURCE LINES 8-44 .. image-sg:: /examples_gallery/advanced_pdes/images/sphx_glr_solver_comparison_001.png :alt: Deviation: 8.5e-05, 0.00018, 9e-05, 9e-05, 9.2e-05, explicit Euler solver, explicit, adaptive Runge-Kutta solver, implicit solver, Crank-Nicolson solver, Adam-Bashforth solver, scipy solver :srcset: /examples_gallery/advanced_pdes/images/sphx_glr_solver_comparison_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Diagnostic information for explicit Euler solver: {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.0017259110000082956, 'tracker': 4.823999998393447e-05, 'compilation': 6.067702561000004}, 'solver_start': '2026-06-12 06:57:43.599366+00:00', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.001767', 't_final': 1.0}, 'package_version': 'unknown', 'solver': {'class': 'EulerSolver', 'pde_class': 'DiffusionPDE', 'dt': 0.001, 'steps': 1000, 'dt_adaptive': False, 'stochastic': False, 'backend': {'name': 'numba', 'implementation': 'numba'}, 'post_step_data': None}} Diagnostic information for explicit, adaptive Runge-Kutta solver: {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.0004832699999894885, 'tracker': 6.897000001515607e-05, 'compilation': 7.257571356999989}, 'solver_start': '2026-06-12 06:57:50.864753+00:00', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.000530', 't_final': 1.0}, 'package_version': 'unknown', 'solver': {'class': 'RungeKuttaSolver', 'pde_class': 'DiffusionPDE', 'dt': 0.19493406912034714, 'steps': 12, 'dt_adaptive': True, 'stochastic': False, 'backend': {'name': 'numba', 'implementation': 'numba'}, 'dt_statistics': {'min': 0.001, 'max': 0.16323357425215385, 'mean': 0.08333333333333333, 'std': 0.05126512350596957, 'count': 12.0}, 'post_step_data': None}} Diagnostic information for implicit solver: {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.008147946999997657, 'tracker': 4.990899999768317e-05, 'compilation': 4.170146201999998}, 'solver_start': '2026-06-12 06:57:55.046180+00:00', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.008192', 't_final': 1.0}, 'package_version': 'unknown', 'solver': {'class': 'ImplicitSolver', 'pde_class': 'DiffusionPDE', 'dt': 0.001, 'steps': 1000, 'dt_adaptive': False, 'stochastic': False, 'backend': {'name': 'numba', 'implementation': 'numba'}, 'function_evaluations': 0, 'post_step_data': None}} Diagnostic information for Crank-Nicolson solver: {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.0125092100000046, 'tracker': 4.765899998915302e-05, 'compilation': 6.265820648000002}, 'solver_start': '2026-06-12 06:58:01.329435+00:00', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.012550', 't_final': 1.0}, 'package_version': 'unknown', 'solver': {'class': 'CrankNicolsonSolver', 'pde_class': 'DiffusionPDE', 'dt': 0.001, 'steps': 1000, 'dt_adaptive': False, 'stochastic': False, 'backend': {'name': 'numba', 'implementation': 'numba'}, 'function_evaluations': 0, 'post_step_data': None}} Diagnostic information for Adam-Bashforth solver: {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 3.792012588999995, 'tracker': 5.5212000006577e-05, 'compilation': 1.8860743110000016}, 'solver_start': '2026-06-12 06:58:03.237261+00:00', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:03.792357', 't_final': 1.0}, 'package_version': 'unknown', 'solver': {'class': 'AdamsBashforthSolver', 'pde_class': 'DiffusionPDE', 'dt': 0.001, 'steps': 1000, 'dt_adaptive': False, 'stochastic': False, 'backend': {'name': 'numba', 'implementation': 'numba'}, 'post_step_data': None}} Diagnostic information for scipy solver: {'controller': {'mpi_run': False, 't_start': 0, 't_end': 1.0, 'profiler': {'solver': 0.665990321999999, 'tracker': 5.815000000097825e-05, 'compilation': 0.0013543710000050169}, 'solver_start': '2026-06-12 06:58:07.033623+00:00', 'successful': True, 'stop_reason': 'Reached final time', 'solver_duration': '0:00:00.666140', 't_final': np.float64(1.0)}, 'package_version': 'unknown', 'solver': {'class': 'ScipySolver', 'pde_class': 'DiffusionPDE', 'dt': 0.001, 'steps': 55, 'stochastic': False, 'backend': {'name': 'numba', 'implementation': 'numba'}}} | .. code-block:: Python import pde # initialize the grid, an initial condition, and the PDE grid = pde.UnitGrid([32, 32]) field = pde.ScalarField.random_uniform(grid, -1, 1) eq = pde.DiffusionPDE() def run_solver(solver, label): """Helper function testing the solver.""" controller = pde.Controller(solver, t_range=1, tracker=None) sol = controller.run(field, dt=1e-3) sol.label = label + " solver" print(f"Diagnostic information for {sol.label}:") print(controller.diagnostics) print() return sol # try different solvers solutions = [ run_solver(pde.EulerSolver(eq), "explicit Euler"), run_solver( pde.RungeKuttaSolver(eq, adaptive=True), "explicit, adaptive Runge-Kutta" ), run_solver(pde.ImplicitSolver(eq), "implicit"), run_solver(pde.CrankNicolsonSolver(eq), "Crank-Nicolson"), run_solver(pde.AdamsBashforthSolver(eq), "Adam-Bashforth"), run_solver(pde.ScipySolver(eq), "scipy"), ] # plot both fields and give the deviation as the title deviations = [(solutions[0] - sol).fluctuations for sol in solutions] title = "Deviation: " + ", ".join(f"{deviation:.2g}" for deviation in deviations[1:]) pde.FieldCollection(solutions).plot(title=title, arrangement=(2, 3)) .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 30.824 seconds) .. _sphx_glr_download_examples_gallery_advanced_pdes_solver_comparison.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: solver_comparison.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: solver_comparison.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: solver_comparison.zip `