In this paper, we develop the Crank-Nicolson finite difference method (C-N-FDM) to solve the linear time-fractional diffusion equation, formulated with Caputo’s fractional derivative. Special attention is given to study the stability of the proposed method which is introduced by means of a recently proposed procedure akin to the standard Von-Neumann stable analysis. Some numerical examples are ...

In this paper we describe a new finite-difference method (FDM) EEG forward problem formulation which accounts for anisotropy of the various head tissues in the volume conductor model of the head. Our proposal, being based on FDM, derives the head model directly from patient’s specific clinical images. We present here the numerical FD formulation and the comparison of the proposed method with a ...

Paper presents an original method suitable for measurement of electric field distribution in liquid dielectrics (nanosecond time domain). Electric field is reconstructed in two steps: 1) multiangular laser scanning of the space between electrodes provides projection for each laser beam, 2) using a numerical algorithm called Modified Aritmetic Reconstruction Technique (MART) electric field is re...

Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of fractional dynamic systems, this paper proposes a scale-dependent finite difference method (S-FDM) in which the non-uniform mesh depends on the time fractional deriva...

This paper presents a comparison of numerical methods for the modelling of pile driving noise in the near field of the pile. The numerical models considered consist of (1) an axisymmetric time domain finite difference method (FDM), developed by the Centre for Marine Science and Technology in the Matlab programming language, and (2) an axisymmetric time domain finite element method (FEM), which ...

The Finite Difference Method (FDM), within the framework of the Meshless Local PetrovGalerkin (MLPG) approach, is proposed in this paper for solving solid mechanics problems. A “mixed” interpolation scheme is adopted in the present implementation: the displacements, displacement gradients, and stresses are interpolated independently using identical MLS shape functions. The system of algebraic e...

A 3D parallel overlapping scheme for viscous incompressible flow problems is presented that combines the finite element method, which is best suited for analysing flow in any arbitrarily shaped flow geometry, with the finite difference method, which is advantageous in terms of both computing time and computer storage. A modified ABMAC method is used as the solution algorithm, to which a sophist...

This paper deals with uncertain parabolic fluid flow problem where the uncertainty occurs due to the initial conditions and parameters involved in the system. Uncertain values are considered as fuzzy and these are handled through a recently developed method. Here the concepts of fuzzy numbers are combined with Finite Difference Method (FDM) and then Fuzzy Finite Difference Method (FFDM) has bee...

Numerical 3D formulations using scalar  and vector A potentials are examined for magnetic fields, with emphasis on the finite difference (FDM) and finite element (FEM) methods using nodal and facet elements. It is shown that for hexahedral elements the FDM equations may be presented in a form similar to the FEM equations; to accomplish this the coefficients defining volume integrals in FEM nee...

This thesis demonstrates the feasibility of using a medial surface transformation as a tool to rapidly approximate the solidification patterns of convex faceted solid models of castings. The medial surface transformation is used to automate the greatest included sphere approach to solidification pattern approximation. The experimental software of this thesis extracts the medial surface transfor...