Parameter determination in a partial differential equation from the overspecified data

Authors:
M. Dehghan
Affiliations:
-
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2005

Citing 6
Cited 8

A Galerkin procedure for the diffusion equation subject to the specification of mass

SIAM Journal on Numerical Analysis
Inversion theory for parameterized diffusion problem

SIAM Journal on Applied Mathematics
Analytical and numerical solutions for a class of nonlocal nonlinear parabolic differential equations

SIAM Journal on Mathematical Analysis
Fully implicit finite differences methods for two-dimensional diffusion with a non-local boundary condition

Journal of Computational and Applied Mathematics
Fully explicit finite-difference methods for two-dimensional diffusion with an integral condition

Nonlinear Analysis: Theory, Methods & Applications
Efficient techniques for the second-order parabolic equation subject to nonlocal specifications

Applied Numerical Mathematics

Determination of a control parameter in a one-dimensional parabolic equation using the moving least-square approximation

International Journal of Computer Mathematics
A numerical method for solution of the two-dimensional sine-Gordon equation using the radial basis functions

Mathematics and Computers in Simulation
Solution of a model describing biological species living together using the variational iteration method

Mathematical and Computer Modelling: An International Journal
Determination of a control parameter in a one-dimensional parabolic equation using the method of radial basis functions

Mathematical and Computer Modelling: An International Journal
The Chebyshev spectral viscosity method for the time dependent Eikonal equation

Mathematical and Computer Modelling: An International Journal
High-order solution of one-dimensional sine-Gordon equation using compact finite difference and DIRKN methods

Mathematical and Computer Modelling: An International Journal
On the determination of the right-hand side in a parabolic equation

Applied Numerical Mathematics
Application of the Ritz-Galerkin method for recovering the spacewise-coefficients in the wave equation

Computers & Mathematics with Applications

Quantified Score

Hi-index	0.98

Visualization

Abstract

The present work is motivated by the desire to obtain numerical solution to a quasilinear parabolic inverse problem. Several schemes are presented for computing the unknown coefficient p(t) in the quasilinear equation u"t = u"x"x + p(t)u + o, in R x (0,T], u(x, 0) = f(x), x @e R = [0,1], u is known on the boundary of R and subject to the integral overspecification over the spatial domain @!"0^1k(x)u(x, t) dx = E(t), 0 @? t @? T, or the overspecification at a point in the spatial domain u(x0,t) = E(t), 0 @? t @? T, where E(t) is known and x"0 is a given point of R. These numerical procedures are developed for identifying the unknown control parameter which produces, at any given time, a desired energy distribution in the spatial domain, or a desired temperature distribution at a given point in the spatial domain. Several finite-difference techniques are used to determine the solution. The accuracy and stability of the methods are discussed and compared. Numerical illustrations are given to show the pertinent features of the developed computational schemes.