MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of
MATLAB Mathematics - SERC - Index of
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Introduction to Initial Value ODE Problems . . . . . . . . . . . . . . . 5-4<br />
Solvers for Explicit and Linearly Implicit ODEs . . . . . . . . . . . . 5-5<br />
Examples: Solving Explicit ODE Problems . . . . . . . . . . . . . . . . 5-9<br />
Solver for Fully Implicit ODEs . . . . . . . . . . . . . . . . . . . . . . . . . 5-15<br />
Example: Solving a Fully Implicit ODE Problem . . . . . . . . . . 5-16<br />
Changing ODE Integration Properties . . . . . . . . . . . . . . . . . . . 5-17<br />
Examples: Applying the ODE Initial Value Problem Solvers . 5-18<br />
Questions and Answers, and Troubleshooting . . . . . . . . . . . . . 5-43<br />
Initial Value Problems for DDEs . . . . . . . . . . . . . . . . . . . . . . . 5-49<br />
DDE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-49<br />
Introduction to Initial Value DDE Problems . . . . . . . . . . . . . . 5-50<br />
DDE Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-51<br />
Solving DDE Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-53<br />
Discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-57<br />
Changing DDE Integration Properties . . . . . . . . . . . . . . . . . . . 5-60<br />
Boundary Value Problems for ODEs . . . . . . . . . . . . . . . . . . . 5-61<br />
BVP Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-62<br />
Introduction to Boundary Value ODE Problems . . . . . . . . . . . 5-63<br />
Boundary Value Problem Solver . . . . . . . . . . . . . . . . . . . . . . . . 5-64<br />
Changing BVP Integration Properties . . . . . . . . . . . . . . . . . . . 5-67<br />
Solving BVP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-68<br />
Using Continuation to Make a Good Initial Guess . . . . . . . . . 5-72<br />
Solving Singular BVPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-80<br />
Solving Multipoint BVPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-84<br />
Partial Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . 5-89<br />
PDE Function Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-89<br />
Introduction to PDE Problems . . . . . . . . . . . . . . . . . . . . . . . . . 5-90<br />
<strong>MATLAB</strong> Partial Differential Equation Solver . . . . . . . . . . . . 5-91<br />
Solving PDE Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-94<br />
Evaluating the Solution at Specific Points . . . . . . . . . . . . . . . . 5-99<br />
Changing PDE Integration Properties . . . . . . . . . . . . . . . . . . 5-100<br />
Example: Electrodynamics Problem . . . . . . . . . . . . . . . . . . . . 5-100<br />
Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-106<br />
iv<br />
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