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2010•Journal of King Saud University - ScienceOpen access

The block by block method for the numerical solution of the nonlinear two-dimensional Volterra integral equations

Farshid Mirzaee, Zinat Rafei

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Abstract

In this study, an efficient method is presented for solving nonlinear two-dimensional Volterra integral equations of the second kind. Using block by block method, nonlinear two-dimensional Volterra integral equations reduce to a algebraic equations. Also a theorem is proved for convergence analysis. Numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method.

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What this paper is about

In this study, an efficient method is presented for solving nonlinear two-dimensional Volterra integral equations of the second kind. Using block by block method, nonlinear two-dimensional Volterra integral equations reduce to a algebraic equations. Also a theorem is proved for convergence analysis. Numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method.

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OpenAlex reports 15 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this study, an efficient method is presented for solving nonlinear two-dimensional Volterra integral equations of the second kind. Using block by block method, nonlinear two-dimensional Volterra integral equations reduce to a algebraic equations. Also a theorem is proved for convergence analysis. Numerical examples are presented and results are compared with the analytical solution to demonstrate the validity and applicability of the method.

Key concepts: Volterra integral equation, Block (permutation group theory), Algebraic equation, Integral equation, Nonlinear system, Mathematics, Convergence (economics), Applied mathematics

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