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Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind
School of Sciences, Shanghai Institute of Technology, Shanghai, China
School of Sciences, Shanghai Institute of Technology, Shanghai, China
- 1 School of Sciences, Shanghai Institute of Technology, Shanghai, China
- 2 School of Sciences, Shanghai Institute of Technology, Shanghai, China
Advances in Pure Mathematics·Volume 05 (2015)·Pages 672–682·Published 7 September 2015·DOI10.4236/apm.2015.511061
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Abstract
Using the Picard iteration method and treating the involved integration by numerical quadrature formulas, we propose a numerical scheme for the second kind nonlinear Volterra integral equations. For enlarging the convergence region of the Picard iteration method, multistage algorithm is devised. We also introduce an algorithm for problems with some singularities at the limits of integration including fractional integral equations. Numerical tests verify the validity of the proposed schemes.
KeywordsVolterra Integral EquationPicard Iteration MethodNumerical IntegrationMultistage Scheme
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