Nonlinear higher-order transient solver for magnetic fluid hyperthermia

The article is devoted to numerical methods for transient solution of Pennes’ bioheat equation as required for Magnetic Fluid Hyperthermia (MFH) modeling. Special attention has been paid to the role of non-linearity of blood perfusion and its influence on temperature distribution. The authors show that the higher-order time integration algorithms are highly advised for this type of problem, which should be classified as a stiff one. Popular low-order solvers give very different solutions. Furthermore, the application of adaptive time stepping scheme reduces calculation time and raises the efficiency of the simulation software.