Caputo and Grünwald-Letnikov derivatives,Ĭitation: Abdul Samad, Imran Siddique, Fahd Jarad.Stability and convergence analysis are also discussed. The accuracy of the suggested scheme is analyzed by using $ L_\infty $-norm. Riesz fractional derivative and Grünwald-Letnikov fractional derivative techniques are used to deal the space fractional derivative terms while the time-fractional derivatives are iterated by Caputo derivative method. The meshfree RBF method base on the Gaussian function and is used to test the numerical results of the time-space fractional PDE problems. In this article, the meshfree numerical scheme, Radial basis function (RBF) is discussed for some time-space fractional PDEs. Different numerical techniques have been adopted to deal the multi-term FPDEs. Used as class notes for graduate courses at Northwestern University, Illinois Institute of Technology, and Vanderbilt University, this book will appeal to both mathematics and engineering graduate students.Fractional partial differential equations (PDEs) have key role in many physical, chemical, biological and economic problems. A good balance is supplied between the necessary theory and implementation in terms of many MATLAB programs, with examples and applications to illustrate key points. Meshfree approximation methods, such as radial basis function and moving least squares method, are discussed from a scattered data approximation and partial differential equations point of view.
The emphasis here is on a hands-on approach that includes MATLAB routines for all basic operations. Whereas other works focus almost entirely on theoretical aspects or applications in the engineering field, this book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. Meshfree approximation methods are a relatively new area of research, and there are only a few books covering it at present.
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