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Advanced Documentation: NDSolve
Overview
Introduction
Design
Features Common time stepping Data encapsulation Method hierarchy User extensibility Method classes Automatic selection and user controllability Shared features Some basic methods Acknowledgements
ODE Integration Methods
Methods
ExplicitRungeKutta
Introduction Example Method comparison Coefficient plug-in Method plug-in Stiffness Step control revisited Option summary
ImplicitRungeKutta
Introduction Coefficients Examples Option summary
SymplecticPartitionedRungeKutta
Introduction Rounding error reduction Examples Available methods Automatic order selection Option summary
Controller methods
Composition and Splitting
DoubleStep
Introduction Examples Option summary
Extrapolation
Introduction Extrapolation Base methods Implementation issues Examples Fine tuning Option summary
FixedStep
OrthogonalProjection
Introduction Examples Option summary Implementation
Projection
StiffnessSwitching
Submethods
ExplicitEuler ExplicitMidpoint ExplicitModifiedEuler LinearlyImplicitEuler LinearlyImplicitMidpoint LinearlyImplicitEuler LocallyExact
Extensions
Method Plug-in Framework
Introduction Classical Runge-Kutta EventLocator Adams methods
Partial Differential Equations
The Numerical Method Of Lines
Introduction Spatial Derivative Approximations
Finite Differences NDSolve`FiniteDifferenceDerivative Pseudospectral derivatives Accuracy and convergence of finite difference approximations Differentiation Matrices
Boundary Conditions Spatial Error Estimates
Overview A-priori error estimates A-posteriori error estimates Controlling the grid selection
Boundary Value Problems
Chasing
Differential-Algebraic Equations
IDA
NDSolve`StateData
Creating NDSolve`StateData objects
ProcessEquations Reinitialize
Iterating Solutions
Getting Solution Functions
NDSolve`StateData methods
Further Reading
References
