MATLAB Mathematics - SERC - Index of

5 Differential Equations
2 Pass the options structure to bvp4c as follows:
sol = bvp4c(odefun,bcfun,solinit,options)
For a complete description of the available options, see the reference page for
bvpset.
Note For other ways to improve solver efficiency, check “Using Continuation
to Make a Good Initial Guess” on page 8-72 and the tutorial, “Solving
Boundary Value Problems for Ordinary Differential Equations in MATLAB
with bvp4c,” available at http://www.mathworks.com/bvp_tutorial.
Solving BVP Problems
This section describes:
• The process for solving boundary value problems using bvp4c
• Finding unknown parameters
• Evaluating the solution at specific points
Example: Mathieu’s Equation
This example determines the fourth eigenvalue of Mathieu's Equation. It
illustrates how to write second-order differential equations as a system of two
first-order ODEs and how to use bvp4c to determine an unknown parameter λ .
The task is to compute the fourth ( q = 5 ) eigenvalue λ of Mathieu's equation
y′′ + ( λ – 2 q cos 2x)y
= 0
Because the unknown parameter λ is present, this second-order differential
equation is subject to three boundary conditions
y( 0) = 1
y′ ( 0) = 0
y′ ( π) = 0
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