Journal ArticleDOI
A fully-Galerkin method for the numerical solution of an inverse problem in a parabolic partial differential equation
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In this paper, a fully-Galerkin approach to the coefficient recovery (parameter identification) problem for a linear parabolic partial differential equation is introduced, where the forward problem is discretised with a sinc basis in the temporal domain and a finite element basis in a spatial domain.Abstract:
A fully-Galerkin approach to the coefficient recovery (parameter identification) problem for a linear parabolic partial differential equation is introduced. The forward problem is discretised with a sinc basis in the temporal domain and a finite element basis in the spatial domain. Tikhonov regularisation is applied to deal with the ill-posedness of the inverse problem. In the solution of the resulting nonlinear optimisation problem, advantage is taken of the diagonalisation solution procedure used for the discretised forward problem. An example with noisy data is included.read more
Citations
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Journal ArticleDOI
Sinc-collocation method for solving astrophysics equations
Kourosh Parand,A. Pirkhedri +1 more
TL;DR: In this paper, Sinc-Collocation method for solving Lane-Emden Equation (LESE) is proposed and it is found that Sinc procedure converges with the solution at an exponential rate.
Journal ArticleDOI
The use of Sinc-collocation method for solving multi-point boundary value problems
Abbas Saadatmandi,Mehdi Dehghan +1 more
TL;DR: In this article, the Sinc-collocation method was used to reduce the computation of solution of multi-point boundary value problems to algebraic equations, and it is well known that Sinc procedure converges to the solution at an exponential rate.
Journal ArticleDOI
Sinc-collocation method for solving the Blasius equation
TL;DR: In this paper, the sinc-collocation method is applied for solving Blasius equation which comes from boundary layer equations and it is well known that sinc procedure converges to the solution at an exponential rate.
Journal ArticleDOI
Convergence of approximate solution of system of Fredholm integral equations
TL;DR: The exponential convergence rate of the Sinc-collocation method is proved and the system of integral equations is reduced to an explicit system of algebraic equations.
Journal ArticleDOI
Collocation method using sinc and Rational Legendre functions for solving Volterra’s population model
TL;DR: In this paper, two approximate methods to solve Volterra's population model for population growth of a species in a closed system were proposed. But the proposed methods have been established based on collocation approach using Sinc functions and Rational Legendre functions.
References
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Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
Journal ArticleDOI
Practical Approximate Solutions to Linear Operator Equations When the Data are Noisy
TL;DR: It is shown that the weighted cross-validation estimate of $\hat \lambda $ estimates the value of $\lambda $ which minimizes $({1 / n) E\sum
olimits_{j = 1}^n {[(\mathcal{K}f_{n,\lambda } )(t_j ) - (\mathcal(K)f)(t-j )]} ^2 $ .
Journal ArticleDOI
A Hessenberg-Schur method for the problem AX + XB= C
TL;DR: A new method is proposed which differs from the Bartels-Stewart algorithm in that A is only reduced to Hessenberg form, and the resulting algorithm is between 30 and 70 percent faster depending upon the dimensions of the matrices A and B.
Journal ArticleDOI
Numerical Methods Based on Whittaker Cardinal, or Sinc Functions
TL;DR: The authors summarizes the results known to date for using sine functions composed with other functions as bases for approximations in numerical analysis, including quadrature, approximate evaluation of transforms, and approximate solution of differential and integral equations.