The Use of the Odd-Even Hopscotch Algorithm for a Thermal Shock Problem

Unusual behavior has been observed in the odd-even hopscotch solution of the heat conduction equation with discontinuous initial data. If the initial approximation at the point adjacent to the discontinuity is explicit, a wave-like disturbance can propagate through the solution domains, resulting in very poor accuracy. This paper examines this unusual behavior of the odd-even hopscotch solution for a thermal shock problem.