We discuss the design of parallel algorithms to solve elliptic problems on multi-clusters computers. Multi-clusters can be seen as two-level parallel architecture machines, since communication between clusters are usually much slower than communication or access to memory within each of the clusters. We introduce special algorithms that use two levels of parallelism and match the multi-cluster ...

Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two-dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed...

This comparative study of fractional nonlinear Burger’s equations and their systems has been done using two efficient analytical techniques. The generalized schemes the proposed techniques for suggested problems are obtained in a very sophisticated manner. numerical examples have solved Laplace residual power series method Elzaki transform decomposition method. results compared through graphs t...

*Correspondence: [email protected] 1Department of Mathematical Sciences, University of Karachi, Karachi, 75270, Pakistan Full list of author information is available at the end of the article Abstract The aim of this article is to introduce the Laplace-Adomian-Padé method (LAPM) to the Riccati differential equation of fractional order. This method presents accurate and reliable results and has ...

This work suggests a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving nonlinear homogeneous andnonhomogeneous time-fractional gas dynamics equations. The FHATM is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian poly...

This research introduces a novel approach that combines the conformable double Laplace–Sumudu transform (CDLST) and iterative method to handle nonlinear partial problems considering some given conditions, we call this new (CDLSI) method. Furthermore, state discuss main properties basic results related proposed technique. The provides approximate series solutions converge closed form of exact so...

In this paper, the solution methodology of higher-order linear fractional partial deferential equations (FPDEs) as mentioned in eqs (1) and (2) below Caputo definition relies on a new analytical method which is called Laplace-residual power series (L-RPSM). The main idea our proposed technique to convert original FPDE Laplace space, then apply residual (RPSM) by using concept limit obtain solut...

Abstract HIV/AIDS is a fatal illness that weakens the immune system of body, making victim susceptible to several opportunistic infections. The analysis and numerical simulation proposed epidemic model with vertical transmission was carried out. disease free endemic equilibrium were obtained basic reproduction number established. Numerical simulations using homotropy perturbation method employe...

in this paper, we propose an algorithm for numerical solving an inverse non-linear diusion problem. in additional, the least-squares method is adopted tond the solution. to regularize the resultant ill-conditioned linear system ofequations, we apply the tikhonov regularization method to obtain the stablenumerical approximation to the solution. some numerical experiments con-rm the utility of...