MATLAB Mathematics - SERC - Index of

Boundary Value Problems for ODEs
Note The demo threebvp contains the complete code for this example and
solves the problem for λ = 2, n = 0.05, and several values of κ. The demo
uses nested functions to place all functions required by bvp4c in a single
M-file and to communicate problem parameters efficiently. To run this
example, type threebvp at the MATLAB command prompt.
The demo takes you through the following steps:
1. Determine the Interfaces and Divide the Interval of Integration Into
Regions
Introducing an interface point at xc = 1 divides the problem into two regions
in which the solutions remain smooth. The differential equations for the two
regions are
Region 1:
v' = (C - 1)/n
C' = (v * C - x)/ η
Region 2:
0 ≤ x ≤ 1
1 ≤ x ≤ λ
v' = (C - 1)/n
C' = (v * C - 1)/ η
Note that the interface xc = 1 is included in both regions. At xc = 1, bvp4c
produces a left and right solution. These solutions are denoted as v(1 - ), C(1 - )
and v(1 + ), C(1 + ) respectively.
2. Determine the Boundary Conditions
Solving two first order differential equations in two regions requires imposing
four boundary conditions. Two of these conditions come from the original
formulation; the others enforce the continuity of the solution across the
interface xc = 1:
v(0) = 0
C( λ ) 1 = 0
v(1-) v(1+) = 0
C(1-) C(1+) = 0
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