Application of general Lagrange scaling functions for evaluating the approximate solution time-fractional diffusion-wave equations

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.

2 1.Department of Mathematics, Anand International College of Engineering, Jaipur 303012, Rajesthan, India. 2. Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE. 3. International Center for Basic and Applied Sciences, Jaipur, 302029, India.

Abstract

This manuscript provides an efficient technique for solving time-fractional diffusion-wave equations using general Lagrange scaling functions (GLSFs). In GLSFs, by selecting various nodes of Lagrange polynomials, we get various kinds of orthogonal or non-orthogonal Lagrange scaling functions. The general Riemann-Liouville fractional integral operator (GRLFIO) of GLSFs is obtained generally. General Riemann-Liouville fractional integral operator of the general Lagrange scaling function is calculated exactly using the Hypergeometric functions. The operator extraction method is precisely calculated and this has a direct impact on the accuracy of our method. The operator and optimization method are implemented to convert the problem to a set of algebraic equations. Also, error analysis is discussed. To demonstrate the efficiency of the numerical scheme, some numerical examples are examined.

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References

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Computational Methods for Differential Equations
Volume 13, Issue 2
March 2025
Pages 450-465

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History

  • Receive Date: 28 October 2023
  • Revise Date: 03 March 2024
  • Accept Date: 27 March 2024

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