Concentrated Heat Sources in the Heat Conducting Rod

The paper shall demonstrate how concentrated source terms can be included by Delta functions in models with distributed parameters and, moreover, that the abstraction of sharply concentrated quantities leads to decisive numeric advantages. The system of differential equations loses its stiffness here at the method of lines. The eigenvalues of the Jacobian matrix (A-matrix) show that it becomes stiffer with decreasing ε since the heat capacity of the source is reduced spatially. The regarded case of concentrated heat sources in the heat conducting rod is of exemplary character for partial differential equations with the time variable, one independent space variable, and spatially concentrated sources.