NUMERICAL TREATMENT OF NON-MONOTONIC BLOW-PROBLEMS BASED ON SOME NON-LOCAL TRANSFORMATIONS

We consider the numerical treatment of blow-up problems having non -monotonic singular solutions that tend to infinity at some point in the domain. The use of standard numerical methods for solving problems with blow-up solutions can lead to significant errors. The reason being that solutions of such problems have singularities whose positions are unknown in advance. To be able to integrate such non -monotonic blow-up problems, we describe and use a method of non -local transformations. To show the efficiency of the method, we present a comparison of exact and numerical solutions in addition to some comparison with the work of other authors.