WOLFRAM|DEMONSTRATIONS PROJECT

Jacobi Polynomials in an Orthogonal Collocation Method

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order
2
3
4
5
6
7
8
9
10
11
12
13
geometry
rectangular
cylindrical
spherical
order
polynomials
1
1-5
2
x
2
21
4
x
-14
2
x
+1
Partial differential equations in rectangular, cylindrical, and spherical coordinates with symmetric boundary conditions occur in many fields of science and engineering. It is often possible to solve such equations using an orthogonal collocation method with roots of Jacobi polynomials as the points of collocation.