Topic 15.1: Finite-Difference Method (Maple)

Introduction Notes Theory HOWTO Examples Engineering Error Questions Matlab Maple

Given the constant-coefficient boundary value problem

c₂ y⁽²⁾(t) + c₁ y⁽¹⁾(t) + c₀ y(2)(t) = f y(a) = y_a
y(b) = y_b

we can solve such a system in Maple as follows:

c[2] := 1.0;
c[1] := 4.0;
c[0] := 2.0;
f := 0.0;
n := 10;
a := 1.0;
b := 3.0;
ya := 4.0;
yb := 2.0;
h := (b - a) / n;
low := 2*c[2] - h*c[1];
diag := 2*h^2*c[0] - 4*c[2];
up := 2*c[2] + h*c[1];
vec := 2*h^2*f;
M := Matrix( n - 1, n - 1 );
v := Vector( n - 1 );
M[1, 1] := diag;
M[1, 2] := up;
v[1] := vec - ya*low;

for i from 2 to n - 2 do
    M[i, i - 1] := low;
    M[i, i] := diag;
    M[i, i + 1] := up;
    v[i] := vec;
end do:

M[n - 1, n - 2] := low;
M[n - 1, n - 1] := diag;
v[n - 1] := vec - yb*up;

y := LinearAlgebra[LinearSolve]( M, v );