In this study, a mathematical model has been developed for the second order hyperbolic one-dimensional time fractional Telegraph equation (TFTE). The fractional derivative has been described in the Caputo sense. The governing equations have been solved by a recent reliable semi-analytic method known as the reduced differential transformation method (RDTM). The method is a powerful mathematical technique for solving wide range of problems. Using RDTM method, it is possible to find exact solution as well as closed approximate solution of any ordinary or partial differential equation. Three numerical examples of TFTE have been provided in order to check the effectiveness, accuracy and convergence of the method. The computed results are also depicted graphically.

In this paper, a numerical solution of two dimensional nonlinear coupled viscous Burger equation is discussed with appropriate initial and boundary conditions using the modified cubic B-spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B-spline as a basis function in the differential quadrature method. Thus, the coupled Burger equation is reduced into a system of ordinary differential equations. An optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme is applied for solving the resulting system of ordinary differential equations. The accuracy of the scheme is illustrated by taking two numerical examples. Computed results are compared with the exact solutions and other results available in literature. Obtained numerical result shows that the described method is efficient and reliable scheme for solving two dimensional coupled viscous Burger equation.

Purpose: The purpose of this paper is to present a modified form of trigonometric cubic B-spline (TCB) collocation method to solve nonlinear Fisher’s type equations. Taylor series expansion is used to linearize the nonlinear part of the problem. Five examples are taken for analysis. The obtained results are better than those obtained by some numerical methods as well as exact solutions. It is noted that the modified form of TCB collocation method is an economical and efficient technique to approximate the solution PDEs. The authors also carried out the stability analysis which proves that the method is unconditionally stable. Design/methodology/approach: The authors present a modified form of TCB collocation method to solve nonlinear Fisher’s type equations. Taylor series expansion is used to linearize the nonlinear part of the problem. The authors also carried out the stability analysis. Findings: The authors found that the proposed method results are better than those obtained by some numerical methods as well as exact solutions. It is noted that the modified form of TCB collocation method is an economical and efficient technique to approximate the solution PDEs. Originality/value: The authors propose a new method, namely, modified form of TCB collocation method. In the authors’ best knowledge, aforesaid method is not proposed by any other author. The authors used this method to solve nonlinear Fisher’s type equations and obtained more accurate results than the results obtained by other methods.

In this paper, an implicit logarithmic finite difference method (I-LFDM) is implemented for the numerical solution of one dimensional coupled nonlinear Burgers’ equation. The numerical scheme provides a system of nonlinear difference equations which we linearise using Newton's method. The obtained linear system via Newton's method is solved by Gauss elimination with partial pivoting algorithm. To illustrate the accuracy and reliability of the scheme, three numerical examples are described. The obtained numerical solutions are compared well with the exact solutions and those already available.