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In this article, a numerical technique is proposed for the solution of time fractional mobile-immobile advectiondispersion equation. Time fractional derivative is considered in the Caputo sense. The spatial and temporal derivatives are approximated based on parametric cubic spline and quadrature formula, respectively. The proposed technique is unconditionally stable and convergence is analyzed using Fourier series method. Numerical evidences confirm the efficiency of the proposed numerical technique. K E Y W O R D S convergence, mobile-immobile equation, parametric cubic spline, stability, time fractionalNumer Methods Partial Differential Eq. 2018;00:00-00.wileyonlinelibrary.com/journal/num

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In this paper, non-polynomial spline method for solving one dimensional nonlinear Benjamin-Bona-Mahony-Burgers equation is presented. Stability analysis of the present method is analyzed by means of Von Neumann process and the method is proven to be unconditionally stable. Truncation error of the proposed method is also discussed. Few numerical evidences are given to prove the validation of the proposed method.

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