We have developed a three level implicit method for solution of the Helmholtz equation. Using the cubic spline in space and finite difference in time directions. The approach has been modied to drive Numerov type nite difference method. The method yield the tri-diagonal linear system of algebraic equations which can be solved by using a tri-diagonal solver. Stability and error estimation of the...

The general Numerov method employed to numerically solve ordinary differential equations of second order was adapted with a special focus on solving Schrödinger's equation. By formulating a hierarchy of novel stencil expressions for the numerical treatment of the Laplace operator in one, two and three dimensions the method could not only be simplified over the standard Numerov scheme. The impro...

In this paper, we propose a new high order Numerov type three-level implicit compact discretization on a non-uniform mesh for the solution of one-space dimensional non-linear hyperbolic partial differential equation of the form utt = uxx + g(x, t, u, ux, ut) subject to appropriate initial and Dirichlet boundary conditions. We use only three evaluations of the function g and three grid points at...

The following integration methods for special second-order ordinary differential equations are studied: leapfrog, implicit midpoint, trapezoid, Störmer–Verlet, and Cowell–Numerov. We show that all are members, or equivalent to members, of a one-parameter family of schemes. Some methods have more than one common form, and we discuss a systematic enumeration of these forms. We also present a stab...

In this article, we present an analytical direct method, based on a Numerov three-point scheme, which is sixth order accurate and has a linear execution time on the grid dimension, to solve the discrete one-dimensional Poisson equation with Dirichlet boundary conditions. Our results should improve numerical codes used mainly in self-consistent calculations in solid state physics.