A practical chebyshev collocation method for differential equations

Abstract

This paper describes a method for solving ordinary and partial differential equations in Chebyshev series. The main feature of the method, which is based on the collocation principle, (Lanczos [8]) is that it solves the problem of differentiating a Chebyshev series directly by the use of a stable recurrence relation. As a practical consequence the method is very simple and can easily be coded into a general-purpose program for solving some differential equations.

Keywords:

• Chebyshev
• collocation
• ordinary
• partial
• derivative
• stability
• elliptic
• hyperbolic
• parabolic
• elimination
• zeros
• coefficient
• iteration
• differential equation
• boundary-value problem
• initial-value problem
• truncation error
• fundamental solution
• spline function
• variation of parameters