Department of Mathematics, Islamic Azad University, Central Tehran Branch, Iran
Abstract
The spline collocation method is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)\times(nN+3n)$ of integro-differential equations. This approximation reduces the system of integro-differential equations to an explicit system of algebraic equations. At the end, some examples are presented to illustrate the ability and simplicity of the method.
Ebrahimi, N., & Rashidinia, J. (2016). Spline Collocation for system of Fredholm and Volterra integro-differential equations. Journal of Mathematical Modeling, 3(2), 189-218.
MLA
Nehzat Ebrahimi; Jalil Rashidinia. "Spline Collocation for system of Fredholm and Volterra integro-differential equations". Journal of Mathematical Modeling, 3, 2, 2016, 189-218.
HARVARD
Ebrahimi, N., Rashidinia, J. (2016). 'Spline Collocation for system of Fredholm and Volterra integro-differential equations', Journal of Mathematical Modeling, 3(2), pp. 189-218.
VANCOUVER
Ebrahimi, N., Rashidinia, J. Spline Collocation for system of Fredholm and Volterra integro-differential equations. Journal of Mathematical Modeling, 2016; 3(2): 189-218.
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