An Effective Computational Approach by Hybrid Functions Operational Matrix for Solving Mixed Kind of the Partial Integro-Differential Equations
Subject Areas : Statistics
1 - Department of Mathematic, Malard Branch, Islamic Azad University, Tehran, Iran.
Keywords: چند جمله ای برنشتاین دو بعدی, معادلات دیفرانسیل انتگرال دیفرانسیل ولترا - فردهلم با مشتقات جزیی, ماتریس عملیاتی, توابع بلوک پالس,
Abstract :
In the present paper, a new method is introduced for the approximate solution of two-dimensional mixed Volterra-Fredholm Partial integro-differential equations with initial conditions using twodimensional hybrid Bernstein polynomials and Block-Pulse functions. For this purpose, an operational matrix of product and integration of the cross-product and differentiation are introduced that essentially of hybrid functions. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations.. The use of these operational matrices simplifies considerably the structure of the computational used for a set of algebraic equations methods for the solution of partial integro-differential equations. Convergence analysis and some numerical results are presented to illustrate the effectiveness and accuracy of the method.
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