A third-order in time numerical IMEX-type algorithm for the StokesDarcy system for flows in fluid saturated karst aquifers is proposed and analyzed. A novel third-order Adams-Moulton scheme is used for the discretization of the dissipative term whereas a third-order explicit Adams-Bashforth scheme is used for the time discretization of the interface term that couples the Stokes and Darcy compon...

Locally refined meshes impose severe stability constraints on explicit time-stepping methods for the numerical simulation of time dependent wave phenomena. Local time-stepping methods overcome that bottleneck by using smaller time-steps precisely where the smallest elements in the mesh are located. Starting from classical Adams-Bashforth multi-step methods, local time-stepping methods of arbitr...

In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using Caputo fractional derivative. We solve non-linear fractional-order system containing six differential equations understand ASR. For proving existence unique solution, use some recent novel properties Mittag–Leffler function along with fixed point theory. The stability proposed is als...

The bidomain model is a system of partial differential equations used to model the propagation of electrical potential waves in the myocardium. It is composed of coupled parabolic and elliptic partial differential equations, as well as at least one ordinary differential equation to model the ion activity through the cardiac cell membranes. The purpose of this paper is to propose and analyze sev...

This paper explored the impact of population symmetry on spread and control a norovirus epidemic. The study proposed mathematical model for epidemic that takes into account asymptomatic infected individuals vaccination effects using non-singular fractional operator Atanganaa–Baleanu Caputo (ABC). Fixed point theory, specifically Schauder Banach’s fixed was used to investigate existence uniquene...

An analysis is reported here for three-time level integration methods following the global spectral analysis (GSA) described in High Accuracy Computing Methods , T.K. Sengupta, Cambridge Univ. Press, USA. The focus is on the second order Adams–Bashforth (AB2) and the extrapolation in time (EXT2) methods. Careful distinction is made for the first time step at t = 0 by either Euler forward or fou...

Background: Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are most prevalent types cancer. Methods: In this work, fractional modeling presented which describes dynamics cancer treatment mixed therapies (immunotherapy chemotherapy). Mathematical mode...

Boundary Layer Flow past a stretching surface with constant wall temperature, of a nanofluid is studied for heat transfer characteristics. The system of partial differential equations describing such a flow is subjected to similarity transformations gives rise to a boundary value problem involving a system of ordinary differential equations. This system is solved by a shooting method. Effect of...

In recent years Atangana and Baleanu proposed a new fractional derivative with non-singular non-local kernel, this paper formulate fragmentary request numerical TB model AtanganaBaleanu (AB derivative). We figured the basic reproduction number ( R0 ) assessment of boundary dependent on genuine information Khyber Pakhtunkhwa Pakistan, Initially we present fundamental properties model, existence ...

Many different numerical models exist for solving the parabolic wave equation. Hardin and Tappert[2] suggested a split-step algorithm in conjunction with the fast Fourier Transform (FFr) method. Lee and Papadakis[3] used a scheme which is based on the predictor-corrector technique of Adams-Bashforth; Lee, Botseas and Papadakis[4] introduced an implicit finitedifference scheme. Chan, Shen and Le...