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.
Background information, solver capabilities and algorithms, and example summary.
This example uses
bvp4c with two different initial guesses to find both solutions to a BVP problem.
This example shows how to use
bvp4c to solve a boundary value problem with an unknown parameter.
This example shows how to solve a multipoint boundary value problem, where the solution of interest satisfies conditions inside the interval of integration.
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.
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.
This example shows how to use continuation to gradually extend a BVP solution to larger intervals.