Solver Library¶
PathSim provides a comprehensive suite of numerical integrators for solving ordinary differential equations.
Explicit Runge-Kutta Methods¶
Fast, non-iterative solvers ideal for non-stiff problems.
First-order explicit forward Euler method, simplest integrator for basic problems.
Classic fourth-order Runge-Kutta method with excellent accuracy-to-cost ratio.
Strong Stability Preserving RK method, 2nd order with 2 stages.
Strong Stability Preserving RK method, 3rd order with 3 stages.
Strong Stability Preserving RK method, 3rd order with 4 stages.
Adaptive Runge-Kutta Methods¶
Embedded methods with automatic step-size control for efficient integration.
Fehlberg’s 2nd/1st order adaptive method for simple non-stiff problems.
3rd/2nd order adaptive method from Bogacki and Shampine.
4th/5th order adaptive method (Fehlberg), widely used classic solver.
5th/4th order adaptive method (Cash-Karp) with optimized error coefficients.
5th/4th order adaptive method (Dormand-Prince), often the default choice for non-stiff problems.
Verner’s 6th/5th order adaptive method for high-accuracy requirements.
7th/8th order adaptive method (Fehlberg) for very high precision applications.
8th/7th order adaptive method (Dormand-Prince) for extreme accuracy demands.
Implicit Methods¶
Iterative solvers for stiff differential equations and algebraic-differential systems.
Backward Differentiation Formulas (fixed step) for stiff problems with strong stability.
Gear’s method for stiff differential equations, adaptive timestepping variants of BDF.
2nd order Diagonally Implicit Runge-Kutta method, A-stable and SSP-optimal.
3rd order Diagonally Implicit Runge-Kutta method, L-stable.
Explicit first stage DIRK, 3rd/2nd order adaptive method.
Explicit first stage DIRK, 4th order for stiff problems.
Explicit first stage DIRK, 4th/3rd order adaptive method.
Explicit first stage DIRK, 5th/4th order adaptive high-accuracy solver.
Explicit first stage DIRK, 8th/5th order adaptive for very high precision.
Special Solvers¶
Time-independent steady-state solver for finding DC operating points and equilibria.
Base Classes¶
Base class for all numerical integrators with core integration functionality.
Base class for Runge-Kutta family methods with tableau-based implementation.