Topic：Solving second-order nonlinear boundary value problem under nonlinear boundary conditions by an fast convergence iterative method
Speaker：Prof. Zhonglun Guo (National Taiwan Ocean University)
Abstarct: The second-order boundary value problem under nonlinear boundary conditions is solved by an iterative numerical method in this paper. We introduce eigenvalues and the corresponding test functions, such that a weak-form integral equation is developed. Then by expanding the numerical solution in terms of the weighted test functions and using the orthogonality, which together with the separated linear boundary conditions, we can obtain the closed-form expansion coefficients with the aid of Drazin inversion formula. When we derive the iterative scheme by putting the time-varying terms and the nonlinear boundary terms on the right-hand sides to solve the nonlinear boundary conditions problem, it is convergent very fast and also provides very accurate numerical solutions. Some examples with multiple solutions are worked out.