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Numerical Solution of Two-Dimensional Nonlinear Stochastic Itô-Volterra Integral Equations by Applying Block Pulse Functions
School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
- 1 School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
- 2 School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
- 3 School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
- 4 School of Mathematics and Statistics, Hubei Normal University, Huangshi, China
Advances in Pure Mathematics·Volume 09 (2019)·Pages 53–66·Published 14 February 2019·DOI10.4236/apm.2019.92004
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Abstract
This paper investigates the numerical solution of two-dimensional nonlinear stochastic It ô -Volterra integral equations based on block pulse functions. The nonlinear stochastic integral equation is transformed into a set of algebraic equations by operational matrix of block pulse functions. Then, we give error analysis and prove that the rate of convergence of this method is efficient. Lastly, a numerical example is given to confirm the method.
KeywordsBlock Pulse FunctionsIntegration Operational MatrixStochastic Itô-Volterra Integral Equations
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