A Radial Basis Function Collocation Method for Space-dependent Inverse Heat Problems
Muhammad Nawaz Khan, Imtiaz Ahmad, Hijaz Ahmad
Abstract
In this study, a radial basis function collocation method (RBFCM) is proposed for the numerical treatment of inverse space-wise dependent heat source problems. Multiquadric radial basis function is applied for spatial discretization whereas for temporal discretization Runge-Kutta method of order four is employed. Numerical experiments for one, two and three-dimensional cases are included to test the efficiency and accuracy of the suggested method. Both non-rectangular and rectangular geometries with uniform and non-uniform points are taken into consideration and the obtained results are compared with the exact as well as with the techniques presented in recent literature.
Topics & Concepts
DiscretizationRadial basis functionCollocation (remote sensing)Basis functionMathematicsBasis (linear algebra)Collocation methodSpace (punctuation)Function (biology)Mathematical analysisInverseApplied mathematicsInverse problemGeometryComputer scienceDifferential equationArtificial neural networkOrdinary differential equationOperating systemEvolutionary biologyBiologyMachine learningNumerical methods in inverse problemsNumerical methods in engineeringHeat Transfer and Optimization