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In this article, we focus on the numerical study of one and two dimensional higher order multi-term time fractional partial differential equations. In the adopted strategy, the temporal fractional derivative is replaced via well known L 1 formula and the integer order space derivatives are approximated by truncated one and two dimensional wavelet series. The fascinating nature of the scheme is to use collocation approach which convert the governing equations to the system of algebraic equations from which the wavelet coefficients can be calculated. Next, stability of the proposed scheme is investigated theoretically which is also the fundamental subject of the current work. Further computational convergence rate is computed which predicts that the order is approximately two. The scheme is applied to solve one dimensional beam models (fourth order partial differential equations) and two dimensional fissured rock models (Sobolev equations). Efficiency of the scheme is examined with the help of various error norms such as I ∞ , I r m s and I 2. Simulations indicate pretty much good results from which we can say that the scheme is suitable and robust for both one and two dimensional problems. [ABSTRACT FROM AUTHOR]

In this paper, a wavelet based collocation method is formulated for an approximate solution of (1 + 1)- and (1 + 2)-dimensional time fractional diffusion wave equations. The main objective of this study is to combine the finite difference method with Haar wavelets. One and two dimensional Haar wavelets are used for the discretization of a spatial operator while time fractional derivative is approximated using second order finite difference and quadrature rule. The scheme has an excellent feature that converts a time fractional partial differential equation to a system of algebraic equations which can be solved easily. The suggested technique is applied to solve some test problems. The obtained results have been compared with existing results in the literature. Also, the accuracy of the scheme has been checked by computing L 2 and L ∞ error norms. Computations validate that the proposed method produces good results, which are comparable with exact solutions and those presented before. [ABSTRACT FROM AUTHOR]

A numerical scheme based on Haar wavelets coupled with finite differences is suggested to study variable order time fractional partial differential equations (TFPDEs). The technique is tested on (1 + 1)-dimensional advection dispersion and (1 + 2)-dimensional advection diffusion equations. In the proposed scheme, time fractional derivative is firstly approximated by quadrature formula, and then finite differences are combined with one and two dimensional Haar wavelets. With the help of suggested method the TFPDEs convert to a system of algebraic equations which is easily solvable. Also convergence of the proposed scheme has been discussed which is an important part of the present work. For validation, the obtained results are matched with earlier work and exact solutions. Computations illustrate that the proposed scheme has better outcomes. [ABSTRACT FROM AUTHOR]