this paper presents discrete galerkin method for obtaining the numerical solution of higher even-order integro-differential equations with variable coefficients. we use the generalized jacobi polynomials with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. numerical results are presented to demonstrate the effectiven...

a simple new closed form of the green function for axisymmetric magnetostatic problemsis found analytically in cylindrical coordinates. the result is verified by applying several examples.

in this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. we applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. the main properties of deterministic difference schemes,...

Fourth-order combined compact finite difference scheme is given for solving the time fractional convection–diffusion–reaction equation with variable coefficients. We introduce the flux as a new variable and transform the original equation into a system of two equations. Compact difference is used as a high-order approximation for spatial derivatives of integer order in the coupled partial diffe...

Non-Fourier models of heat conduction have been increasingly considered in the last years in the modeling of microscale heat transfer in engineering and biomedical problems. Models that incorporate time lags in the heat flux and/or the temperature gradient result in heat conduction modeling equations in the form of partial differential equations with delay, while some approximations may yield p...

We prove the unique solvability in weighted Sobolev spaces of non-divergence form elliptic and parabolic equations on a half space with the homogeneous Neumann boundary condition. All the leading coefficients are assumed to be only measurable in the time variable and have small mean oscillations in the spatial variables. Our results can be applied to Neumann boundary value problems for stochast...

Abstract. In this paper we study the Borel summability of formal solutions with a parameter of first order semilinear system of partial differential equations with n independent variables. In [Singular perturbation of linear systems with a regular singularity, J. Dynam. Control. Syst. 8 (2002), 313–322], Balser and Kostov proved the Borel summability of formal solutions with respect to a singul...

semilinear stochastic evolution equations with multiplicative l'evy noise are considered‎. ‎the drift term is assumed to be monotone nonlinear and with linear growth‎. ‎unlike other similar works‎, ‎we do not impose coercivity conditions on coefficients‎. ‎we establish the continuous dependence of the mild solution with respect to initial conditions and also on coefficients. ‎as corollarie...