Orthogonal cubic splines for the numerical solution of nonlinear parabolic partial differential equations.

In this paper, a new orthogonal basis for the space of cubic splines has been introduced. A linear combination of cubic orthogonal splines is considered to approximate the functions in which the coefficients are calculated with numerically stable formulae. Applications to the numerical solutions of some parabolic partial differential equations are given, in which the approximations are obtained using the first and second integral of orthogonal splines which leads to an efficient solution procedure.

A mathematical system of COVID-19 disease model: Existence, uniqueness, numerical and sensitivity analysis.

A compartmental mathematical model of spreading COVID-19 disease in Wuhan, China is applied to investigate the pandemic behaviour in Iran. This model is a system of seven ordinary differential equations including individual behavioural reactions, governmental actions, holiday extensions, travel restrictions, hospitalizations, and quarantine. We fit the Chinese model to the Covid-19 outbreak in Iran and estimate the values of parameters by trial-error approach.

A Novel Effective Approach for Solving Fractional Nonlinear PDEs.

The present work introduces an effective modification of homotopy perturbation method for the solution of nonlinear time-fractional biological population model and a system of three nonlinear time-fractional partial differential equations. In this approach, the solution is considered a series expansion that converges to the nonlinear problem. The new approximate analytical procedure depends only on two iteratives.

An efficient method for systems of variable coefficient coupled Burgers' equation with time-fractional derivative.

A new homotopy perturbation method (NHPM) is applied to system of variable coefficient coupled Burgers' equation with time-fractional derivative. The fractional derivatives are described in the Caputo fractional derivative sense. The concept of new algorithm is introduced briefly, and NHPM is examined for two systems of nonlinear Burgers' equation.