Sixth-Kind Chebyshev and Bernoulli Polynomial Numerical Methods for Solving Nonlinear Mixed Partial Integrodifferential Equations with Continuous Kernels
A. M. Al‐Bugami, M.A. Abdou, A. M. S. Mahdy
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.