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Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients

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  • Yongqiang Yang
  • Yunpeng Ma
  • Lifeng Wang

Abstract

A numerical method for solving a class of fractional partial differential equations with variable coefficients based on Legendre polynomials is proposed. A fractional order operational matrix of Legendre polynomials is also derived. The initial equations are transformed into the products of several matrixes by using the operational matrix. A system of linear equations is obtained by dispersing the coefficients and the products of matrixes. Only a small number of Legendre polynomials are needed to acquire a satisfactory result. Results obtained using the scheme presented here show that the numerical method is very effective and convenient for solving fractional partial differential equations with variable coefficients.

Suggested Citation

  • Yongqiang Yang & Yunpeng Ma & Lifeng Wang, 2015. "Legendre Polynomials Operational Matrix Method for Solving Fractional Partial Differential Equations with Variable Coefficients," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-9, June.
    • Handle: RePEc:hin:jnlmpe:915195
    DOI: 10.1155/2015/915195
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