An Effective Computational Approach by Hybrid Functions Operational Matrix for Solving Mixed Kind of the Partial Integro-Differential Equations
محورهای موضوعی : آمار
1 - گروه ریاضی، دانشگاه آزاد اسلامی واحد ملارد ، تهران ، ایران.
کلید واژه: Volterra&ndash, Block pulse functions, Two-dimensional Bernstein polynomials, Fredholm Partial integro-differential equations, Operational matrix,
چکیده مقاله :
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.
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.
[1] محمود بهروزی فر (1398) ارائه دو مدل برای تحلیل عددی جواب معادلات دیفرانسیل-انتگرال کسری و مقایسه آنها، مجله پژوهش های نوین در ریاضی، مهر و آبان 1398. 48-31.
[2] فرشید میرزایی، سیده فاطمه حسین، سحر علیپور (1399) حل عددی مدل ریاضی انتشار بیماریهای عفونی بر پایه چندجمله ایهای برنشتاین انتقال یافته ، مجله پژوهش های نوین در ریاضی، خردادو تیر 1399. 38-29.
[3] بنت الهدا هاشمی، مرتضی خدابین (1396) بسط سری انتگرال‌های وینر به کمک توابع بلاک پالس، مجله پژوهش های نوین در ریاضی، فروردین و اردیبهشت 1396. 32-25.
[4] S. Kazem, J.A. Rad, K. Parand, A meshless method on non-Fickian flows with mixing length growth in porous media based on radial basis functions: A comparative study, Computers and Mathematics with Applications 64, 399–412 (2012).
[5] P. Hepperger, Hedging electricity swaptions using partial integro-differential equations, Stochastic Processes And Their Applications, 122, 600-622 (2012).
[6] M. Dehghan and R. Salehi, The numerical solution of thenon-linear integro-differential equations based on the meshless method, Journal of Computational and Applied Mathematics, 236, 9, 2367–2377, (2012).
[7]Y.N. Grigoriev, N.H. Ibragimov, V.F. Kovalev and S.V. Meleshko, Symmetries of Integro-Differential Equations: With Applications in Mechanics and Plasma Physics, Springer (2010).
[8] F.Abeergel and R. Tachet, A nonlinear partial integro-differential equation from mathematical finance, AIMS, 10, 10-20 (2010).
[9] K.S. Zadeh, An integro-partial differential equation for modeling biofluids flow in fractured biomaterials, Theoretical Biology, 273, 72-79 (2011).
[10] Y. Lin, C.Xu, Finite difference/spectral approximations for the time-fractional diffusion equation, Comput. Phys, 225, 1533-1552 (2007).
[11]S. Larsson, V. Thomée, L. Wahlbin, Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method, Math Comput, 67, 45-71 (1998).
[12]S.Saha Ray , S. Behera, Two-dimensional wavelets operational method for solving Volterra weakly singular partial integro-differential equations, Journal of Computational and Applied Mathematics 366, 112411 (2020).
[13] S. Behera, S.Saha Ray, An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations, Applied Mathematics and Computation 367, 124771 (2020).
[14] K. Maleknejad, K. Mahdiani, Solving nonlinear mixed Volterra–Fredholm integral equations with two-dimensional block-pulse functions using direct method, Comm. Nonlinear Sci. Numer. Simul. 16, 3512–3519 (2011).
[15] K. Maleknejad and M. Tavassoli Kajani, Solving second kind integral equations by Galerkin methods with hybrid Legendre and block-pulse function, Applied Mathematics and Computation, 145(2-3), 623-629, (2003).
