6,359 research outputs found
An ADI extrapolated Crank-Nicolson orthogonal spline collocation method for nonlinear reaction-diffusion systems: a computational study
An alternating direction implicit (ADI) orthogonal spline collocation (OSC)
method is described for the approximate solution of a class of nonlinear
reaction-diffusion systems. Its efficacy is demonstrated on the solution of
well-known examples of such systems, specifically the Brusselator, Gray-Scott,
Gierer-Meinhardt and Schnakenberg models, and comparisons are made with other
numerical techniques considered in the literature. The new ADI method is based
on an extrapolated Crank-Nicolson OSC method and is algebraically linear. It is
efficient, requiring at each time level only operations where
is the number of unknowns. Moreover,it is shown to produce
approximations which are of optimal global accuracy in various norms, and to
possess superconvergence properties
A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions
In this paper, the fractional order of rational Bessel functions collocation
method (FRBC) to solve Thomas-Fermi equation which is defined in the
semi-infinite domain and has singularity at and its boundary condition
occurs at infinity, have been introduced. We solve the problem on semi-infinite
domain without any domain truncation or transformation of the domain of the
problem to a finite domain. This approach at first, obtains a sequence of
linear differential equations by using the quasilinearization method (QLM),
then at each iteration solves it by FRBC method. To illustrate the reliability
of this work, we compare the numerical results of the present method with some
well-known results in other to show that the new method is accurate, efficient
and applicable
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Accepted versio
Tchebychev Polynomial Approximations for Order Boundary Value Problems
Higher order boundary value problems (BVPs) play an important role modeling
various scientific and engineering problems. In this article we develop an
efficient numerical scheme for linear order BVPs. First we convert the
higher order BVP to a first order BVP. Then we use Tchebychev orthogonal
polynomials to approximate the solution of the BVP as a weighted sum of
polynomials. We collocate at Tchebychev clustered grid points to generate a
system of equations to approximate the weights for the polynomials. The
excellency of the numerical scheme is illustrated through some examples.Comment: 21 pages, 10 figure
Factorizing the Stochastic Galerkin System
Recent work has explored solver strategies for the linear system of equations
arising from a spectral Galerkin approximation of the solution of PDEs with
parameterized (or stochastic) inputs. We consider the related problem of a
matrix equation whose matrix and right hand side depend on a set of parameters
(e.g. a PDE with stochastic inputs semidiscretized in space) and examine the
linear system arising from a similar Galerkin approximation of the solution. We
derive a useful factorization of this system of equations, which yields bounds
on the eigenvalues, clues to preconditioning, and a flexible implementation
method for a wide array of problems. We complement this analysis with (i) a
numerical study of preconditioners on a standard elliptic PDE test problem and
(ii) a fluids application using existing CFD codes; the MATLAB codes used in
the numerical studies are available online.Comment: 13 pages, 4 figures, 2 table
Inverse heat conduction problems by using particular solutions
Based on the method of fundamental solutions, we develop in this paper a new computational method to solve two-dimensional transient heat conduction inverse problems. The main idea is to use particular solutions as radial basis functions (PSRBF) for approximation of the solutions to the inverse heat conduction problems. The heat conduction equations are first analyzed in the Laplace transformed domain and the Durbin inversion method is then used to determine the solutions in the time domain. Least-square and singular value decomposition (SVD) techniques are adopted to solve the ill-conditioned linear system of algebraic equations obtained from the proposed PSRBF method. To demonstrate the effectiveness and simplicity of this approach, several numerical examples are given with satisfactory accuracy and stability.Peer reviewe
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