A BOUNDARY ELEMENT METHOD BASED SOLUTION PROCEDURE FOR NONLINEAR BOUNDARY-VALUE-PROBLEMS

This paper describes a technique for the solution of non-linear boundary value problems in one dimension based on the boundary element method. The nonlinearity is handled by a quasilinearization over subintervals or elements within the main domain. The weighting functions used are the solutions to the one dimensional diffusion operator or the solutions to the adjoint differential equation to the original problem. The paper also describes the development of a computer code to handle the numerical aspects of the problem. A number of illustrative problems are solved using this computer code and it is demonstrated that the method is very robust and leads to accurate numerical results for both the dependent variable and its derivative at the nodal points. A method of estimating the accuracy of the solution is also presented. A number of problems for which the boundary element method is likely to be particularly suitable are pointed out. © 1990.