Abstract

A collocation method with space–time radial polynomials for solving two–dimensional inverse heat conduction problems (IHCPs) is presented. The space–time radial polynomial series function is developed for spatial and temporal discretization of the government equation within the space–time domain. Because boundary and initial data are assigned on the space–time boundaries, the numerical solution of the IHCP can be approximated by solving the inverse boundary value problem in the space–time domain without using the time–marching scheme. The inner, source, and boundary points are uniformly distributed using the proposed outer source space–time collocation scheme. Since all partial derivatives up to order of the problem’s operator of the proposed basis functions are a series of continuous functions, which are nonsingular and smooth, the numerical solutions are obtained without using the shape parameter. Numerical examples for solving IHCPs with missing both parts of initial and boundary data are carried out. The results of our study are then compared with those of other collocation methods using multiquadric basis function. Results illustrate that highly accurate recovered temperatures are acquired. Additionally, the recovered temperatures on inaccessible boundaries with high accuracy can be acquired even 1/5 portion of the entire space–time boundaries are inaccessible.

## Keywords

Space–time

Collocation method

Inverse heat conduction problem

Radial polynomials

Radial basis function

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