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Sixth-Kind Chebyshev and Bernoulli Polynomial Numerical Methods for Solving Nonlinear Mixed Partial Integrodifferential Equations with Continuous Kernels
Faculty
Science
Year:
2023
Type of Publication:
ZU Hosted
Pages:
1-14
Authors:
Amr Mohamed Samy Mohammed Mahdi
Staff Zu Site
Abstract In Staff Site
Journal:
Journal of Function Spaces Hindawi
Volume:
2023
Keywords :
Sixth-Kind Chebyshev , Bernoulli Polynomial Numerical Methods
Abstract:
In the present paper, a new efficient technique is described for solving nonlinear mixed partial integrodifferential equations with continuous kernels. Using the separation of variables, the nonlinear mixed partial integrodifferential equation is converted to a nonlinear Fredholm integral equation. Then, using different numerical methods, the Bernoulli polynomial method and the Chebyshev polynomials of the sixth kind, the nonlinear Fredholm integral equation has been reduced into a system of nonlinear algebraic equations. The Banach fixed-point theory is utilized in order to have a conversation about the nonlinear mixed integral equation’s solution, namely, its existence and uniqueness. In addition, we talk about the convergence and stability of the solution. Finally, a comparison between the two different methods and some other famous methods is presented through various examples. All the numerical results are calculated and obtained using the Maple software.
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