A New Computational Method Based on Bernstein Operational Matrices for Solving Two-Dimensional Linear Stochastic Volterra Integral Equations
| Autor: | Morteza Khodabin, Mohsen Fallahpour, Reza Ezzati |
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| Rok vydání: | 2019 |
| Předmět: |
Basis (linear algebra)
Applied Mathematics 01 natural sciences Bernstein polynomial Integral equation Volterra integral equation 010101 applied mathematics Algebraic equation symbols.namesake Operational matrix Product (mathematics) 0103 physical sciences Convergence (routing) symbols Applied mathematics 0101 mathematics 010301 acoustics Analysis Mathematics |
| Zdroj: | Differential Equations and Dynamical Systems. 30:873-884 |
| ISSN: | 0974-6870 0971-3514 |
| Popis: | This paper is concerned with obtaining the approximate numerical solution of two-dimensional linear stochastic Volterra integral equation by using two-dimensional Bernstein polynomials as basis. Properties of these polynomials and operational matrix of integration together with the product operational matrix are utilized to transform the integral equation to a matrix equation which corresponds to a system of linear algebraic equations with unknown Bernstein coefficients. Some theorems are included to show the convergence and advantage of the proposed method. The numerical example illustrates the efficiency and accuracy of the method. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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