A Least Squares Differential Quadrature Method for a Class of Nonlinear Partial Differential Equations of Fractional Order

Constantin Bota, Bogdan Căruntu, Dumitru Ţucu, Marioara Lăpădat and Mădălina Sofia Paşca
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Constantin Bota: Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania
Bogdan Căruntu: Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania
Dumitru Ţucu: Department of Mechanical Machinery, Equipment and Transport, Politehnica University of Timişoara, 300222 Timişoara, Romania
Marioara Lăpădat: Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania
Mădălina Sofia Paşca: Department of Mathematics, Politehnica University of Timişoara, 300006 Timişoara, Romania

Mathematics, 2020, vol. 8, issue 8, 1-12

Abstract: In this paper a new method called the least squares differential quadrature method (LSDQM) is introduced as a straightforward and efficient method to compute analytical approximate polynomial solutions for nonlinear partial differential equations with fractional time derivatives. LSDQM is a combination of the differential quadrature method and the least squares method and in this paper it is employed to find approximate solutions for a very general class of nonlinear partial differential equations, wherein the fractional derivatives are described in the Caputo sense. The paper contains a clear, step-by-step presentation of the method and a convergence theorem. In order to emphasize the accuracy of LSDQM we included two test problems previously solved by means of other, well-known methods, and observed that our solutions present not only a smaller error but also a much simpler expression. We also included a problem with no known exact solution and the solutions computed by LSDQM are in good agreement with previous ones.

Keywords: fractional differential equations; nonlinear partial differential equations; analytical approximate solution; differential quadrature method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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