Sixth-Kind Chebyshev and Bernoulli Polynomial Numerical Methods for Solving Nonlinear Mixed Partial Integrodifferential Equations with Continuous Kernels
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....
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2023-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2023/6647649 |
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| Summary: | 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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| ISSN: | 2314-8888 |