[PDF] Top 20 High order locally one dimensional methods for solving two dimensional parabolic equations

... a high order ADI difference scheme and a high order LOD difference scheme, respectively, for solving the two-dimensional parabolic equations with Dirichlet ... See full document

... with parabolic equations such as proliferation of gas, the penetration of liquids, heat conduction and spread of impurities in semicon- ductor ...cal methods including the finite difference method, ... See full document

... of high order differential ...differential equations. Lepik [21] used two-dimensional Haar wavelets to solve diffusion equation and Poisson ... See full document

... numerical methods, there are many methods to solve Poisson equation, such as Ritz- Galerkin method [1], finite difference method [2], finite volume method and so on [3, ...for two-dimensional ... See full document

... numerical methods are proposed for solving fractional cable equation for example, Liu et ...solved one dimensional fractional cable equation by two implicit numerical methods ... See full document

... explicit two-steps methods to solve one-dimensional heat ...the one-dimensional heat equation demonstrating the convergence, high accuracy and unconditional stability of ... See full document

... The orthogonal spline collocation (OSC) method has developed into a robust and valu- able technique for solving many kinds of partial differential equations [34–38]. The pop- ularity of OSC is due to its ... See full document

... j = − q  p are unknown constants to be determined. Substituting Equation (2.3) into Equation (2.2) yields an algebraic equation in powers of the Exp-function. Then, to determine the values of m and p, we balance the li- ... See full document

... These methods are employed for linear fractional differential equations, and cannot be used for nonlinear ...for solving such ...fractional order. Chen et al. [] proposed two numerical ... See full document

... for solving inverse problems have been proposed [32]-[29] and among the various methods such as: Tikhonov regularization [31], iterative regularization [2], mollification [22], BFM (Base Function Method) ... See full document

... In this section we utilize the equation error cost functional in the inverse problem algorithm. The equation error approach has two distinct advantages over the OLS approach. Firstly, it leads to a convex ... See full document

... by two symmetric and the accuracy of contact surface and left expansion waves with further validation from the numerical ...exactly one-dimensional stationary contact ...- order to 3 rd ... See full document

... differential equations to get a system of ODEs with time ...such methods is poor in the spatial ...in one and two ...the high accuracy and exponential convergence that can be ... See full document

... Kantorovich L.V., Akilov G.P. (1982). Functional Analysis. Pergamon press Ltd.and Nauka publisher. Karoui A., Jawahdou A. (2010). Existence and approximate L p and contin-uous solutions of nonlinear integral ... See full document

... The boundary condition simply requires that glioma cells are not allowed to migrate outside of the human tissue. Assume that the tumour has grown to about 4000 cells as a local mass before it begins to diffuse. We used ... See full document

... (18) Using the relation between cos (.) and sin (.) functions the number of coefficients is easily reduced. Equating each coefficient of powers of multiplication cos (.) and sin (.) functions in the resultant equation, ... See full document

... In order to integrate nanomaterials with different properties into functional systems, much attention has been focused on branched CNTs ...A high-intensity electron beam was used to join crossed CNTs ... See full document

... The numerical results for solving Gq and G are displayed in Table 1. Here CPU ”q and CPU ” denotes the computational time (s) for solving Gq and G respectively. After deriving Gq , we need to multiply R # E ... See full document

... The remaining part of this paper is organized as follows. Section 2 is devoted to some essential concepts about the stable method for Gaussian RBF interpolation based on eigenfunction expansions. In Section 3, the ... See full document

... the back values of each block. Ibrahim et al. (2008) developed the block method by adding a fixed coefficients block backward differentiation formules to solve first order ODEs. Ibrahim et al. (2011) also ... See full document