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Mathematica
Overview
Advanced Numerical Differential Equation Solving in
Mathematica
Introduction
Overview
The Design of the NDSolve Framework
Features
Common time stepping
Data encapsulation
Method hierarchy
User extensibility
Method classes
Automatic selection and user controllability
Shared features
Some basic methods
ODE Integration Methods
Methods
ExplicitRungeKutta
ImplicitRungeKutta
SymplecticPartitionedRungeKutta
Controller methods
Composition and Splitting
DoubleStep
EventLocator
Extrapolation
FixedStep
OrthogonalProjection
Projection
StiffnessSwitching
Submethods
ExplicitEuler
ExplicitMidpoint
ExplicitModifiedMidpoint
LinearlyImplicitEuler
LinearlyImplicitMidpoint
LinearlyImplicitModifiedMidpoint
LocallyExact
Extensions
Method Plug-in Framework
Partial Differential Equations
The Numerical Method of Lines
Introduction
Spatial Derivative Approximations
Boundary Conditions
Spatial Error Estimates
Boundary Value Problems
Shooting Method
Chasing Method
Boundary Value Problems with Parameters
Differential-Algebraic Equations
Introduction
IDA Method
Error Control
ScaledVectorNorm
Components and Data Structures
Introduction
Example
Creating NDSolve`StateData Objects
ProcessEquations
Reinitialize
Iterating Solutions
Getting Solution Functions
NDSolve`StateData methods
DifferentialEquations Utility Packages
InterpolatingFunctionAnatomy
NDSolveUtilities
References
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