Integral formulations for 1-D Biharmonic and Second Order Coupled Linear and Nonlinear Boundary Value Problems

Abstract

Integral formulations based on a boundary-domain interpretation of the boundary element method (BEM) are applied to develop the numerical solutions of biharmonic and second order coupled linear and nonlinear boundary value problems. The governing multiple differential equations are converted to their integral analogs by applying the Green’s identity or by double integration. The resulting integral equations are put in matrix form and solved numerically to yield both the primary dependent variable and its spatial derivative. Available benchmark solutions are applied to test the reliability of the formulation. The results are found to be in conformity with the closed form solutions and also accurately represent the physics which the problems represent.