Inverse problems for PDEs, convergence, homotopy iteration, heat conduction, ill-posed problem, error bounds, backward conduction, Error bounds for initial value and initial-boundary value problems involving PDEs, Inverse problems in thermodynamics and heat transfer, Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs, numerics