Boundary Value Problems

Boundary value problem solvers for ordinary differential equations

Boundary value problems (BVPs) are ordinary differential equations that are subject to boundary conditions. Unlike initial value problems, a BVP can have a finite solution, no solution, or infinitely many solutions. The initial guess of the solution is an integral part of solving a BVP, and the quality of the guess can be critical for the solver performance or even for a successful computation. The bvp4c and bvp5c solvers work on boundary value problems that have two-point boundary conditions, multipoint conditions, singularities in the solutions, or unknown parameters. For more information, see Solving Boundary Value Problems.

Plotted solutions of two boundary value problems

Functions

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Solvers

`bvp4c`	Solve boundary value problem — fourth-order method
`bvp5c`	Solve boundary value problem — fifth-order method
`bvpinit`	Form initial guess for boundary value problem solver

Get/Set Options

`bvpget`	Extract properties from options structure created with bvpset
`bvpset`	Create or alter options structure of boundary value problem

Evaluate and Extend Solution

`deval`	Evaluate differential equation solution structure
`bvpxtend`	Form guess structure for extending boundary value solutions

Topics

Solving Boundary Value Problems
Background information, solver capabilities and algorithms, and example summary.
Solve BVP with Two Solutions
This example uses bvp4c with two different initial guesses to find both solutions to a BVP problem.
Solve BVP with Unknown Parameter
This example shows how to use bvp4c to solve a boundary value problem with an unknown parameter.
Solve BVP with Multiple Boundary Conditions
This example shows how to solve a multipoint boundary value problem, where the solution of interest satisfies conditions inside the interval of integration.
Solve BVP with Singular Term
This example shows how to solve Emden's equation, which is a boundary value problem with a singular term that arises in modeling a spherical body of gas.
Solve BVP Using Continuation
This example shows how to solve a numerically difficult boundary value problem using continuation, which effectively breaks the problem up into a sequence of simpler problems.
Verify BVP Consistency Using Continuation
This example shows how to use continuation to gradually extend a BVP solution to larger intervals.