Pseudospectral and high-order finite difference methods are well established for solving time-dependent partial differential equations by the method of lines. The use of highorder spatial discretizations has led in turn to a concomitant interest in high-order time stepping schemes, so that the temporal and spatial errors are of comparable magnitude. Explicit Runge-Kutta methods are widely used ...

We describe a novel 3D finite difference method for solving the anisotropic inhomogeneous Poisson equation based on a multi-component additive implicit method with a 13-point stencil. The serial performance is found to be comparable to the most efficient solvers from the family of preconditioned conjugate gradient (PCG) algorithms. The proposed multicomponent additive algorithm is unconditional...

A unified framework to derive optimized compact schemes for a uniform grid is presented. The scheme coefficients are determined analytically by solving an optimization problem minimize the spectral error subject equality constraints that ensure specified order of accuracy. rigorous stability analysis also We show other types e.g., spatially explicit and biased finite differences, can be generat...

Fractional order partial differential equations, as generalizations of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of application. In this paper we discuss a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equation...

In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind fini...

Long time solutions to the Frank-Kamenetskii partial differential equation modelling a thermal explosion in a vessel are obtained using matrix exponentiation. Spatial derivatives are approximated by high-order finite difference approximations. A forward difference approximation to the time derivative leads to a Lawson-Euler scheme. Computations performed with a BDF approximation to the time der...

Numerical Simulation of three dimensional wave equation is conducted in a cubic domain which contains two parts, part A and part B. Part A of the domain is a I -shaped empty channel, containing air, and part B, containing a solid medium, is the difference between the whole cubic domain and part A. A Dirichlet type boundary condition is specified at the inlet boundary. At all other boundaries of...