A new approach for solving nonlinear Volterra integro-differential equations with Mittag--Leffler kernel
R.M. Ganji
2020Proceedings of the Institute of Mathematics and Mechanics National Academy of Sciences of Azerbaijan47 citationsDOIOpen Access PDF
Abstract
In this work, we consider a general class of nonlinear Volterra integro-differential equations with Atangana-Baleanu derivative. We use the operational matrices based on the shifted Legendre polynomials to obtain numerical solution of the considered equations. By approximating the unknown function and its derivative in terms of the shifted Legendre polynomials and substituting these approximations into the original equation and using the collocation points, the original equation is reduced to a system of nonlinear algebraic equations. An error estimate of the numerical solution is proved. Finally, some examples are included to show the accuracy and validity of the proposed method.
Topics & Concepts
Kernel (algebra)Nonlinear systemMathematicsApplied mathematicsVolterra integral equationVolterra equationsDifferential equationMathematical analysisIntegral equationPure mathematicsPhysicsQuantum mechanicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods