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Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

100%

Ersoy O., Dag I.

Open Physics

2015

vol. 13

issue 1

The solutions of the reaction-diffusion system are given by method of collocation based on the exponential B-splines. Thus the reaction-diffusion systemturns into an iterative banded algebraic matrix equation. Solution of the matrix equation is carried out byway of Thomas algorithm. The present methods test on both linear and nonlinear problems. The results are documented to compare with some earlier studies by use of L∞ and relative error norm for problems respectively.

Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers’ equation

81%

Ay B., Dag I., Gorgulu M. Z.

Open Physics

2015

vol. 13

issue 1

A variant of the subdomain Galerkin method has been set up to find numerical solutions of the Burgers’ equation. Approximate function consists of the combination of the trigonometric B-splines. Integration of Burgers’ equation has been achived by aid of the subdomain Galerkin method based on the trigonometric B-splines as an approximate functions. The resulting first order ordinary differential system has been converted into an iterative algebraic equation by use of the Crank-Nicolson method at successive two time levels. The suggested algorithm is tested on somewell-known problems for the Burgers’ equation.

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2 Open Physics

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2 Dag I.

1 Ay B.

1 Ersoy O.

1 Gorgulu M. Z.

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Numerical solutions of the reaction diffusion system by using exponential cubic B-spline collocation algorithms

Trigonometric quadratic B-spline subdomain Galerkin algorithm for the Burgers’ equation