Malaria is a possibly dangerous infection brought about by a parasite. This infection is more normal in nations with heat and humidities. Because of chromosomal changes, the elements of malaria parasites are very mind-boggling to study up just as for any predictions. A reaction-diffusion model to characterize the elements inside have Malaria contamination with versatile safe reactions is concentrated in this paper. The aim of the paper is to develop and analyze a spectrally accurate pseudospectral method in time and space to find the approximate solution of the reaction-diffusion model. The approximate solution is represented in terms of basis functions. The spectral coefficients are found in such a way that the residual becomes minimum. Error estimates for interpolating polynomials are derived. The computational experiments are carried out to corroborate the theoretical results and to compare the present method with existing methods in the literature. The registered mathematical outcomes are in great concurrence with those generally accessible in the writing. Simple to apply and accomplish exact arrangement in less time is the solid place of the current strategy.

In this paper, the authors approximate the solution of time fractional multi- dimensional Burger’s equation using the time-space Chebyshev pseudospectral method. Caputo fractional derivatives formula is used to illustrate the fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivatives matrices the given problem is reduced to a system of nonlinear algebraic equations. These equations can be solved using Newton’s iterative method. Error analysis of the proposed method for the equation is presented. Model examples of time-fractional Burger’s equation are tested for a set of values of $ \nu $, where $ \nu $ represent the fractional order. For the proposed method, highly accurate numerical results are obtained which are compared with the analytical solution to confirm the accuracy and efficiency of the proposed method.

In this paper, the authors investigate the interaction of soliton waves for multidimensional nonlinear Schrodinger equation (NSE) using time-space Jacobi pseudospectral method. The proposed method is established in both time and space to approximate the solutions and to prove the stability analysis for the equations. Using the Jacobi derivatives matrices the given problem is reduced to a system of nonlinear algebraic equations, which will be solved using Newton’s Raphson method. For numerical experiments, the method is tested on a number of different examples to study the behavior of interaction of two and more than two soliton, single soliton. Moreover, numerical solutions are demonstrated to justify the theoretical results and confirm the expected convergence rate. Comparison of numerical and exact solution is depicted in the form of figures and tables.