In this paper, by considering the two-step Laplace decomposition method and the appearance of noise terms, exact solutions are calculated for nonlinear Abel's integral equation and generalized Abel's integral equation. This new method provides us to find the solutions with lees computation as compared with other methods. The method will be described along with several examples. Mathematics Subj...

In this paper, the two-dimensional Stokes problem is analyzed by the modified collocation Trefftz method (MCTM) and the Laplacian decomposition. The coupled Stokes equations are converted to three Laplace equations by utilizing the Laplacian decomposition and then the boundary-type meshless MCTM is adopted to solve the resultant Laplace equations. The MCTM, free from mesh and numerical quadratu...