Malaysian Journal of Mathematical Sciences, September 2021, Vol. 15, No. 3
A New Approach to Numerical Solution of Nonlinear Partial Mixed Volterra-Fredholm Integral Equations via Two-Dimensional Triangular Functions
Safavi, M., Khajehnasiri, A. A., Jafari, A., and Banar, J.
Corresponding Email: a.khajehnasiri@gmail.com
Received date: 4 March 2020
Accepted date: 27 April 2021
Abstract:
This paper proposes a numerical procedure for solving the nonlinear partial mixed Volterra-Fredholm integro-differential equations by two-dimensional triangular function (2D-TFs). The integration and differentiation in two-dimensional spaces have been presented for an operational matrix on triangular functions, whereas by converting the nonlinear partial mixed Volterra-Fredholm integro-differential equation to a system of algebraic by using these matrices. Some numerical examples, have been proposed to obtain the accuracy and effectiveness of the method.
Keywords: nonlinear equations; partial mixed Volterra-Fredholm integral equations; operational matrix; two-dimensional triangular functions
