On spectral methods for Volterra type integral equations and the convergence analysis
نویسندگان
چکیده
The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicate that the numerical errors (in the infinity norm) will decay exponentially provided that the kernel function and the source function are sufficiently smooth. Numerical results are presented, which confirm the theoretical prediction of the exponential rate of convergence. The result in this work seems to be the first successful spectral approach (with theoretical justification) for the Volterra type equations. AMS(MOS) subject classification. 35Q99, 35R35, 65M12, 65M70
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