A quartic trigonometric tension b-spline algorithm for nonlinear partial differential equation system

The purpose of this study is to construct quartic trigonometric tension (QTT) B-spline collocation algorithms for the numerical solutions of the Coupled Burgers’ equation.

The finite elements method (FEM) is a numerical method for obtaining an approximate solution of partial differential equations (PDEs). The development of high-speed computers enables to development FEM to solve PDEs on both complex domain and complicated boundary conditions. It also provides higher-order approximation which consists of a vector of coefficients multiplied by a set of basis functions. FEM with the B-splines is efficient due both to giving a smaller system of algebraic equations that has lower computational complexity and providing higher-order continuous approximation depending on using the B-splines of high degree.

The result of the test problems indicates the reliability of the method to get solutions to the CBE. QTT B-spline collocation approach has convergence order 3 in space and order 1 in time. So that nonpolynomial splines provide smooth solutions during the run of the program.

There are few numerical methods build-up using the trigonometric tension spline for solving differential equations. The tension B-spline collocation method is used for finding the solution of Coupled Burgers’ equation.