Several studies have presented compact fourth order accurate finite difference approximation for the Helmholtz equation in two or three dimensions. Several of these formulae allow for the wave number k to be variable. Other papers have extended this further to include variable coefficients within the Laplacian which models non-homogeneous materials in electromagnetism. Later papers considered m...

The Ceylon Journal of Science is a peer-reviewed journal published quarterly by the University Peradeniya, Sri Lanka in March, June, September and December. It aimed at publishing high quality research articles on topics related to different disciplines Science. accepts original articles, book reviews, reviews mini-reviews, short communications, opinions, notes, commentaries notes. has its own ...

Based on the exponent transform to eliminate the “convection item” in the equation and the fourth-order compact difference formulas for the first and second derivatives, two chasses of new implicit difference schemes are proposed for solving the one-dimensional convection-diffusion equation. The methods are of order O ( τ2 + h4 ) and O ( τ4 + h4 ) respectively. The former is proved to be uncond...

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation. Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations. For the temporal direction, we utilize the favorable boundary value methods owing to their advantageous stability properties. In addition, the resul...

We propose a formal expansion of multiple relaxation times lattice Boltzmann schemes in terms single infinitesimal numerical variable. The result is system partial differential equations for the conserved moments scheme. presented nonlinear case up to fourth order accuracy. asymptotic corrections nonconserved are developed equilibrium values and differentials moments. Both expansions coupled co...