A Boundary-Type Numerical Procedure to Solve Nonlinear Nonhomogeneous Backward-in-Time Heat Conduction Equations

In this paper, an explicit boundary-type numerical procedure, including a constraint-type fictitious time integration method (FTIM) and two-point boundary solution of the Lie-group shooting (LGSM), is constructed to tackle nonlinear nonhomogeneous backward heat conduction problems (BHCPs). Conventional methods cannot effectively overcome instability solve inverse that lack initial conditions take long calculate, even using different variable transformations regularization techniques. Therefore, explicit-type procedure developed from FTIM LGSM avoid iterations. First, introduced into algorithm. Then, maximum minimum values guess value can be determined linearly at final times. Finally, FTIM, directly iterative BHCPs. Several examples are tested. Based on results shown, obtain approximated achieve stable convergence conditions, if iterations occur. Furthermore, efficiency accuracy better than in previous literature, with increased computational span without technique.