A steady-state and transient finite element model has been developed to approximate, with simple triangular elements, the two-dimensional advection—diffusion equation for practical river surface flow simulations. Essentially, the space—time Crank—Nicolson—Galerkin formulation scheme was used to solve for a given conservative flow-field. Several kinds of point sources and boundary conditions, na...

Diffusion models with constant boundaries and drift function have been successfully applied to model phenomena in a wide range of areas psychology. In recent years, more complex time-dependent space-time-dependent functions gained popularity. One obstacle the empirical theoretical evaluation these is lack simple efficient numerical algorithms for computing their first-passage time distributions...

With an aim to investigate the effect of externally imposed body acceleration on two dimensional,pulsatile blood flow through a stenosed artery is under consideration in this article. The blood flow has been assumed to be non-linear, incompressible and fully developed. The artery is assumed to be an elastic cylindrical tube and the geometry of the stenosis considered as time dependent, and a co...

[1] We present a hybrid method for the numerical solution of advection-diffusion problems that combines two standard algorithms: semi-Lagrangian schemes for hyperbolic advection-reaction problems and CrankNicolson schemes for purely diffusive problems. We show that the hybrid scheme is identical to the two end-member schemes in the limit of infinite and zero Peclet number and remains accurate o...

This contribution proposes two third-order numerical schemes for solving time-dependent linear and non-linear partial differential equations (PDEs). For spatial discretization, a compact fourth-order scheme is deliberated. The stability of the proposed set scalar equation, whereas its convergence specified system parabolic equations. applied to equation systems comprises governing heat mass tra...

Due to the intrinsically initial singularity of solution and discrete convolution form in numerical Caputo derivatives, traditional H1-norm analysis (corresponding case for a classical diffusion equation) time approximations fractional subdiffusion problem always leads suboptimal error estimates (a loss accuracy). To recover theoretical accuracy time, we propose an improved Grönwall inequality ...