# A numerical algorithm based on a new kind of tension B-spline function for solving Burgers-Huxley equation

## Abstract

In this paper, a numerical algorithm based on a new kind of tension B-spline, named hyperbolic-trigonometric tension B-spline method, is applied for solving Burgers-Huxley equation. This method is generated over the space span {sin(tt),cos(tt),sinh(tt),cosh(tt),1,t,...,tn-?5},n =?5, where t is the tension parameter. Properties of it are the same in most of the properties of the usual polynomial B-splines and benefit from some other advantages, as well. Therefore, in this paper, we apply three methods consisting of trigonometric method, hyperbolic tension B-spline method, and our new hyperbolic-trigonometric tension B-spline method, to solve Burgers-Huxley equation. The convergence analysis is discussed. Then, we use some numerical examples to illustrate the accuracy and implementation of the proposed algorithm.

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Alinia, N., Zarebnia, M. A numerical algorithm based on a new kind of tension B-spline function for solving Burgers-Huxley equation. Numer Algor 82, 1121–1142 (2019). https://doi.org/10.1007/s11075-018-0646-4

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### Keywords

• Burgers-Huxley equation
• Tension B-spline
• Hyperbolic-trigonometric
• Collocation method
• Numerical algorithm