Numerical treatment of fractal boundary value problems for heat conduction in polar bear with spatial variation of thermal conductivity

A high-resolution compact discretization scheme for the numerical approximation of two-point nonlinear fractal boundary value problems is presented to study the stationary anomalous diffusion process. Hausdorff derivative is applied to derive the models in fractal media. The proposed scheme solves the nonlinear fractal model and achieves an accuracy of order four by employing only three mesh points in a stencil and consumes short computing time. Numerical simulations with heat conduction in polar bear, convection–diffusion, boundary layer, Bessel’s and Burgers equation in a fractal medium are carried out to illustrate the utility of the scheme and their numerical rate of convergence.