The method of approximate fundamental solutions for axisymmetric problems with Laplace operator

The paper presents a new numerical technique for solving axisymmetric problems with Laplace operator. It is similar to the method of fundamental solutions but it is based on the use of special basis functions which satisfy the majority of the boundary conditions of the problem considered. This reduces the number of unknowns and the size of the collocation matrix considerably. As it is shown in the paper, this technique can also be applied successfully in the cases when the solution domain has infinite boundaries in zz or rr directions. Numerical examples justifying the method are presented.