Computing Open

The neural network trial function method of Legaris et al. (Artificial neural networks for solving ordinary and partial differential equations, IEEE Trans. Neural Netw. 9(5) (1998) 987–1000) requires the specification of a boundary function that matches the boundary values and is finite in the solution domain. We develop a recursive formula for generating a boundary function for up to second-order partial differential equations with Dirichlet boundary conditions in a finite hyper-box domain and with an arbitrary number of dimensions.