Concept explainers
Consider the boundary-value problem
Approximate the solution of the differential equation at the interior points of the region with mesh size h =
The approximate solution of the given differential equation
Answer to Problem 1RE
The approximate solution of the differential equation at the interior points of the region is
Explanation of Solution
Formula used:
Calculation:
Consider the given boundary value problem.
For constructing a mesh with size with
Since
Similarly,
For
From the given boundary conditions
Repeat this for
Since there are less number of unknowns, use Gauss-elimination method to solve the system of equations.
Here, use row column transformations to obtain the values of
Further reduce the matrix as follows.
Therefore, the approximate solution of the differential equation at the interior points of the region is
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Chapter 15 Solutions
Differential Equations with Boundary-Value Problems (MindTap Course List)
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage