|
چکیده
|
This study presents an efficient numerical framework for solving an inverse heat equation problem involving a time-dependent heat source and temperature distribution. The problem incorporates non-classical boundary conditions and integral over-determination conditions, where the latter represents error-contaminated measurements. A time-stepping scheme is employed to discretize the time derivative, while a meshless local collocation method using radial basis functions (RBFs) is applied for spatial discretization. The stability and convergence of the time-discretized approach are rigorously established using the energy method. To address noise in input data, Tikhonov regularization of three orders is implemented, along with a novel approach for determining the optimal regularization parameter. This method outperforms traditional techniques such as the quasi-optimality criterion, L-curve, and discrepancy principle. Numerical experiments validate the approach by demonstrating its accuracy for exact data and stability under noisy conditions, thereby establishing it as a reliable tool for inverse problem-solving.
|