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 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.
Functions
Topics
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.
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.
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.
Verify BVP Consistency Using Continuation
This example shows how to use continuation to gradually extend a BVP solution to larger intervals.