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Khalid Masood

Bio: Khalid Masood is an academic researcher from King Fahd University of Petroleum and Minerals. The author has contributed to research in topics: Inverse problem & Heat equation. The author has an hindex of 5, co-authored 14 publications receiving 84 citations.

Papers
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Journal ArticleDOI
TL;DR: In this paper, an integral representation for the inverse problem is found, from which a formula for initial temperature is derived using Picard's criterion and the singular system of the associated operators.

30 citations

Journal ArticleDOI
TL;DR: In this article, the inverse problem in the heat equation involving the recovery of the initial temperature front measurements of the final temperature is investigated and a regularizing parameter which approximates and regularizes the heat conduction model is proposed.
Abstract: We investigate the inverse problem in the heat equation involving the recovery of the initial temperature front measurements of the final temperature. This problem is extremely ill-posed and it is believed that only information in the first few modes can be recovered by classical methods. We will consider this problem with a regularizing parameter which approximates and regularizes the heat conduction model

13 citations

Journal ArticleDOI
TL;DR: In this paper, a class of numerical schemes based on positivity-preserving Pade approximations were proposed to solve initial inverse problems in the heat equation and applied the proposed numerical schemes on the parabolic heat equation.
Abstract: The classical inverse problem of recovering the initial temperature distribution from the final temperature distribution is extremely ill-posed. We propose a class of numerical schemes based on positivity-preserving Pade approximations to solve initial inverse problems in the heat equation. We also utilize a partial fraction decomposition technique to solve the problem more efficiently when higher order Pade approximations are used. We apply the proposed numerical schemes on the parabolic heat equation. Our aim is to model the problem as a direct problem and use our numerical schemes to recover the initial profile in a stable and efficient way.

11 citations

Journal ArticleDOI
TL;DR: In this paper, a new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques.
Abstract: A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.

10 citations

Journal ArticleDOI
TL;DR: In this paper, the Lie symmetry method is applied to analyze a nonlinear elastic wave equation for longitudinal deformations with third-order anharmonic corrections to the elastic energy, and reductions to second-order ODEs are obtained through invariance under different symmetries.
Abstract: Lie symmetry method is applied to analyze a nonlinear elastic wave equation for longitudinal deformations with third-order anharmonic corrections to the elastic energy. Symmetry algebra is found and reductions to second-order ordinary differential equations (ODEs) are obtained through invariance under different symmetries. The reduced ODEs are further analyzed to obtain several exact solutions in an explicit form. It was observed in the literature that anharmonic corrections generally lead to solutions with time-dependent singularities in finite times. Along with solutions with time-dependent singularities, we also obtain solutions which do not exhibit time-dependent singularities.

10 citations


Cited by
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Book ChapterDOI
01 Jan 1998
TL;DR: In this article, the boundary value problems of mathematical physics can be solved by the methods of the preceding chapters by solving a variety of specific problems that illustrate the principal types of problems that were formulated in Chapter 7.
Abstract: The goal of this final chapter is to show how the boundary value problems of mathematical physics can be solved by the methods of the preceding chapters. This will be done by solving a variety of specific problems that illustrate the principal types of problems that were formulated in Chapter 7. Additional applications are developed in the Exercises. The primary solution method is Fourier’s method of separation of variables and the associated Sturm-Liouville theory of Chapter 8.

530 citations

Proceedings ArticleDOI
22 May 2011
TL;DR: This work studies the spatiotemporal sampling of a diffusion field generated by K point sources, aiming to fully reconstruct the unknown initial field distribution from the sample measurements, and indicates that it is possible to compensate linearly for insufficient spatial sampling densities by oversampling in time.
Abstract: We study the spatiotemporal sampling of a diffusion field generated by K point sources, aiming to fully reconstruct the unknown initial field distribution from the sample measurements. The sampling operator in our problem can be described by a matrix derived from the diffusion model. We analyze the important properties of the sampling matrices, leading to precise bounds on the spatial and temporal sampling densities under which perfect field reconstruction is feasible. Moreover, our analysis indicates that it is possible to compensate linearly for insufficient spatial sampling densities by oversampling in time. Numerical simulations on initial field reconstruction under different spatiotemporal sampling densities confirm our theoretical results.

58 citations

Journal ArticleDOI
TL;DR: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted by as mentioned in this paper, where the authors conducted a comprehensive survey.
Abstract: A comprehensive survey of the literature in the area of numerical heat transfer (NHT) published between 2000 and 2009 has been conducted Due to the immenseness of the literature volume, the survey

58 citations

Journal ArticleDOI
TL;DR: A review of heat transfer literature published in 2004 in English language, including some translations of foreign language papers, is presented in this paper, where papers are grouped into subject-oriented sections and further divided into sub-fields.

56 citations