Boundary Value Problems
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
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.
- Solving Boundary Value Problems
Background information, solver capabilities and algorithms, and example summary.
- Solve BVP with Two Solutions
This example uses
bvp4cwith two different initial guesses to find both solutions to a BVP problem.
- Solve BVP with Unknown Parameter
This example shows how to use
bvp4cto 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.