In this article we have proposed an accurate finite difference method for approximate numerical solution of second order boundary value problem with Dirichlet boundary conditions. There are numerous numerical methods for solving these boundary value problems. Some these methods are more efficient and accurate than others with some advantages and disadvantages. The results in experiment on model...

Random walks can be used to solve the Dirichlet problem – the boundary value problem for harmonic functions. We begin by constructing the random walk in Z and showing some of its properties. Later, we introduce and examine harmonic functions in Z in order to set up the discrete Dirichlet problem. Finally, we solve the Dirichlet problem using random walks. Throughout the paper, we discuss connec...

Let Ω be a bounded C2 domain in R and φ : ∂Ω → R be a continuous map. The Dirichlet problem for the minimal surface system asks whether there exists a Lipschitz map f : Ω → R with f |∂Ω = φ and with the graph of f a minimal submanifold in Rn+m. For m = 1, the Dirichlet problem was solved more than thirty years ago by Jenkins-Serrin [13] for any mean convex domains and the solutions are all smoo...

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...