The radiative transfer equation is an integro-differential equation whose efficient numerical solution requires significant computational resources. In the present study, we seek to unite two powerful techniques in contemporary scientific computing: the discontinuous Galerkin (DG) methods and computation on graphics processing units (GPU) for solving the radiative transfer equation. Significant...

In the recent paper [2], the authors obtained new proofs on the existence and uniqueness of the solution of the Volterra linear equation. Applying their results, in this paper we express the exact and approximate solution of the equation in the field of Mikusi´nski operators, F, which corresponds to an integro–differential equation.

A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

The expected discounted penalty with downside jumps has been extensively studied in Gerber and Shiu(1998), Gerber and Landry(1998), Tsai and Wilmott(2002) and others. In this paper, we study the expected discounted penalty in a perturbed compound Poisson model with two sided jumps. We show that it is always twice continuously differentiable provided that the jump size distribution has a bounded...

Fuzzy integro-differential equations is one of the important parts of fuzzy analysis theory that holds theoretical as well as applicable values in analytical dynamics and so an appropriate computational algorithm to solve them is in essence. In this article, we use parametric forms of fuzzy numbers and suggest an applicable approach for solving nonlinear fuzzy integro-differential equations usi...

In this second part of paper the description of conservative averaging method for partial differential (or integro-differential) equation with discontinuous coefficients in cylinder type domain is given. The conservative averaging is carried out in two orthogonal directions. Different types of boundary conditions are examined. Key-Words: partial differential equations, discontinuous coefficient...

In this paper a numerical technique based on the B-spline method is presented for the solution of Fredholm integro-differential equations. To illustrate the efficiency of the method some examples are introduced and the results are compared with the exact solution.  

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter ~e.g., the temperature! that depends on integrals of the unknown distribution function. The standard approach to solving the resulting nonlinear partial differential equation involves the use of predictor–corrector algorithms, ...