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  • Open Access


    Solvability of the Nonlocal Inverse Parabolic Problem and Numerical Results

    M. J. Huntul1,*, Taki-Eddine Oussaeif2

    Computer Systems Science and Engineering, Vol.40, No.3, pp. 1109-1126, 2022, DOI:10.32604/csse.2022.020175

    Abstract In this paper, we consider the unique solvability of the inverse problem of determining the right-hand side of a parabolic equation whose leading coefficient depends on time variable under nonlocal integral overdetermination condition. We obtain sufficient conditions for the unique solvability of the inverse problem. The existence and uniqueness of the solution of the inverse parabolic problem upon the data are established using the fixed point theorem. This inverse problem appears extensively in the modelling of various phenomena in engineering and physics. For example, seismology, medicine, fusion welding, continuous casting, metallurgy, aircraft, oil and gas… More >

  • Open Access


    Finding the Time-dependent Term in 2D Heat Equation from Nonlocal Integral Conditions

    M.J. Huntul*

    Computer Systems Science and Engineering, Vol.39, No.3, pp. 415-429, 2021, DOI:10.32604/csse.2021.017924

    Abstract The aim of this paper is to find the time-dependent term numerically in a two-dimensional heat equation using initial and Neumann boundary conditions and nonlocal integrals as over-determination conditions. This is a very interesting and challenging nonlinear inverse coefficient problem with important applications in various fields ranging from radioactive decay, melting or cooling processes, electronic chips, acoustics and geophysics to medicine. Unique solvability theorems of these inverse problems are supplied. However, since the problems are still ill-posed (a small modification in the input data can lead to bigger impact on the ultimate result in the… More >

  • Open Access


    Meshless Local Integral Equations Formulation for the 2D Convection-Diffusion Equations with a Nonlocal Boundary Condition

    Ahmad Shirzadi1

    CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.1, pp. 45-64, 2012, DOI:10.3970/cmes.2012.085.045

    Abstract This paper presents a meshless method based on the meshless local integral equation (LIE) method for solving the two-dimensional diffusion and diffusion-convection equations subject to a non-local condition. Suitable finite difference scheme is used to eliminate the time dependence of the problem. A weak formulation on local subdomains with employing the fundamental solution of the Laplace equation as test function transforms the resultant elliptic type equations into local integral equations. Then, the Moving Least Squares (MLS) approximation is employed for discretizing spatial variables. Two illustrative examples with exact solutions being used as benchmark solutions are More >

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