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A local meshless method for the numerical solution of space‐dependent inverse heat problems
Author(s) -
Khan Muhammad Nawaz,
Hussain Iltaf,
Ahmad Imtiaz,
Ahmad Hijaz
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6439
Subject(s) - mathematics , discretization , radial basis function , regularized meshless method , numerical analysis , collocation (remote sensing) , mathematical analysis , inverse problem , collocation method , domain (mathematical analysis) , space (punctuation) , function (biology) , moving least squares , inverse , square root , singular boundary method , geometry , finite element method , differential equation , computer science , boundary element method , philosophy , remote sensing , linguistics , biology , ordinary differential equation , machine learning , evolutionary biology , artificial neural network , thermodynamics , physics , geology
In this paper, a local radial basis function collocation method is proposed for the numerical solution of inverse space‐wise dependent heat source problems. Multiquadric radial basis function is used for spatial discretization. The method accuracy is tested in terms of absolute root mean square and relative root mean square error norms. Numerical tests on a noisy data are performed on both regular domain and irregular domain. To test the efficiency and accuracy of the proposed method, numerical experiments for one‐, two‐, and three‐dimensional cases are performed. Both regular and irregular geometries with uniform and nonuniform points are taken into consideration, and the numerical results are also compared with the existing methods reported in literature.