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Solution of non-linear Klein-Gordan equation with a quadratic non-linear term by adomian decomposition method

Basak K. Ch., Ray P. Ch., Bera R. K.

International Journal of Applied Mechanics and Engineering

2009

Vol. 14, no 3

891-897

Nonlinear PDEs are systematically solved by the decomposition method of Adomian for general boundary conditions described by boundary operator equations. In the present case, the solution of the nonlinear Klein-Gordon equation has been considered as an illustration of the decomposition method of Adomian.

Newton's iteration with a conjugate gradient based decomposition method for an elliptic PDE with a nonlinear boundary condition

Koko J.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 1

13-18

Newton's iteration is studied for the numerical solution of an elliptic PDE with nonlinear boundary conditions. At each iteration of Newton's method, a conjugate gradient based decomposition method is applied to the matrix of the linearized system. The decomposition is such that all the remaining linear systems have the same constant matrix. Numerical results confirm the savings with respect to the computational cost, compared with the classical Newton method with factorization at each step.