Matlab Code For Keller Box Method
the kellerbox method is used for solving the poisson equation. the objective of this research was to develop a method for fast and accurate solution of the nonlinear poisson equation with a smaller model size. the proposed method is based on a fast approximation of the legendre polynomials. the main idea of the proposed method is based on the approximate solution of the legendre polynomials by a truncated series of chebyshev polynomials with a coefficients that are obtained by the iteration method, which is more efficient than the other available methods. it was also shown that the proposed method is more stable and accurate than the existing methods, especially for the cases where the exact solution is close to the solution of the linear poisson equation. the accuracy and computational efficiency of the proposed method were investigated by several benchmark problems, for which the analytical solution is known and the data are obtained by the finite element method. the accuracy of the proposed method was also tested by solving the three dimensional nonlinear poisson equation. the results show that the proposed method can generate highly accurate solutions with a smaller model size than the keller-box method.
the keller-box method and the implicit perturbation method (ipm) are applied to solving the nonlinear poisson equation. the keller-box method is a finite difference method (fdm) which was developed by herbert keller in the 1950s. the keller-box method is used to obtain approximate solutions to the linearized poisson’s equation. the keller-box method is based on the local separation of variables approach and on the solution of the two-dimensional problem of laplace equation. this approach is used to obtain the approximate solution of a nonlinear problem by a linear problem. the implicit perturbation method (ipm) is an iterative method which was introduced by jacques-louis lions and pierre-louis lions to solve some nonlinear problems. the ipm has a wide range of applications in the study of nonlinear partial differential equations. the ipm is based on the homotopy analysis method (ham). the aim of this research is to extend the application of the keller-box method and the ipm to obtain approximate solutions of nonlinear poisson’s equation. the keller-box method and the ipm are applied to the solution of the nonlinear poisson equation for the cases of the constant coefficient and the variable coefficient. the numerical simulations show that the proposed methods can obtain highly accurate solutions with a smaller model size than keller-box method. the performance of the proposed methods was compared with the keller-box method. the computational efficiency of the proposed methods is compared with the keller-box method. it is shown that the proposed method can generate highly accurate solutions with a smaller model size than keller-box method.
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