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.

The purpose of this work is to find the numerical solution of the Caputo time-fractional diffusion equation using the modified cubic exponential B-spline (CExpB-spline) collocation technique. First, the CExpB-spline functions are modified and then used to discretize the space derivatives. Three numerical examples are considered for checking the efficiency and accuracy of the method. The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. Von Neumann stability is carried out which gives the guarantee that the technique is unconditionally stable. The rate of convergence is also obtained. Furthermore, this technique is efficient and requires less storage.

Purpose: A collocation technique based on re-defined quintic B-splines over Crank-Nicolson is presented to solve the Fisher's type equation. We take three cases of aforesaid equation. The stability analysis and rate of convergence are also done.Design/methodology/approach: The quintic B-splines are re-defined which are used for space integration. Taylor series expansion is applied for linearization of the nonlinear terms. The discretization of the problem gives up linear system of equations. A Gaussian elimination method is used to solve these systems.Findings: Three examples are taken for analysis. The analysis gives guarantee that the present method provides much better results than previously presented methods in literature. The stability analysis and rate of convergence show that the method is unconditionally stable and quadratic convergent for Fisher's type equation. Moreover, the present method is simple and easy to implement, so it may be considered as an alternative method to solve PDEs.Originality/value: This work is the original work of authors which is neither published nor submitted anywhere else for publication.