حل عددي معادلات انتگرال - ديفرانسيل فرد هلم - ولتراي غير خطي با استفاده از چند جمله ايهاي متعامد لژاندر

Numerical Solution of Nonlinear Integro-Differential Equations by Using Legendre Orthogonal Polynomials

The main purpose in this article is obtaining an approximate solution with appropriate accuracy for nonlinear integro-differential equations. First, truncated Legendre expansion of the solution of equation is considered, then by using the collocation points, equation and its conditions transform into the system of nonlinear algebraic equations. By solving this system, Legendre expansion unknown coefficients are obtained. Finally, some examples are presented to illustrate the method.