Abstract:

A Chebyshev-collocation spectral method is developed for Volterra type integro-differential equations. The Volterra type integro-differential equation as two linear integral equations of the second kind is rewrited, and the integrand with Lagrange basis functions and the Lagrange basis functions in terms of the Chebyshev polynomials are expanded. An error analysis is conducted based on the L_∞ norm. Numerical results are presented to demonstrate effectiveness of the proposed method.

Key words: Chebyshev-collocation spectral method; integro-differential equations; Lagrange basis function; Chebyshev weight