NANASep 5, 2017

An Efficient Computational Technique based on Cubic Trigonometric B-splines for Time Fractional Burgers' Equation

arXiv:1709.0133645 citations
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This work provides an efficient numerical method for solving time fractional Burgers' equations, which is incremental as it combines existing techniques with a new linearization approach.

The paper develops a linear computational technique using cubic trigonometric B-splines for the time fractional Burgers' equation, achieving unconditional stability and reduced computational cost. Numerical results show the method is more accurate than a parametric spline-based scheme.

This paper presents a linear computational technique based on cubic trigonometric cubic B-splines for time fractional burgers' equation. The nonlinear advection term is approximated by a new linearization technique which is very efficient and significantly reduces the computational cost. The usual finite difference formulation is used to approximate the Caputo time fractional derivative while the derivative in space is discretized using cubic trigonometric B-spline functions. The method is proved to be globally unconditionally stable. To measure the accuracy of the solution, a convergence analysis is also provided. A convergence analysis is Computational experiments are performed to further establish the accuracy and stability of the method. Numerical results are compared with those obtained by a scheme based on parametric spline functions. The comparison reveal that the proposed scheme is quite accurate and effective.

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