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Advanced Numerical Differential Equation Solving in Mathematica
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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
MethodMonitor
Shared Features
Some Basic Methods
ODE Integration Methods
Methods
ExplicitRungeKutta
ImplicitRungeKutta
SymplecticPartitionedRungeKutta
Controller Methods
Composition and Splitting
Submethods
LocallyExact
DoubleStep
EventLocator
Extrapolation
Submethods
ExplicitEuler
ExplicitMidpoint
ExplicitModifiedMidpoint
LinearlyImplicitEuler
LinearlyImplicitMidpoint
LinearlyImplicitModifiedMidpoint
FixedStep
OrthogonalProjection
Projection
StiffnessSwitching
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
Delay Differential Equations
Introduction
Comparison and Contrast with ODEs
Propagation and Smoothing of Discontinuities
Storing History Data
Method of Steps
Examples
Error Control
ScaledVectorNorm
Stiffness Detection
Overview
Introduction
Linear Stability
"StiffnessTest" Method Option
"NonstiffTest" Method Option
Examples
Option Summary
Structured Systems
LotkaVolterra
Introduction
Explicit Euler
Backward Euler
Projection
Splitting
Symplectic Euler
Flows
RigidBody
Introduction
Manifold Generation and Utility Functions
Method Comparison
Adams Multistep Method
Euler and Implicit Midpoint Methods
Orthogonal Projection Method
Projection Method
Projecting One Constraint
Projecting Multiple Constraints
"Splitting" Method
Solution
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
TUTORIAL COLLECTION
Advanced Numerical Differential Equation Solving in
Mathematica
Mathematics and Algorithms
