İkinci mertebeden lineer olmayan parabolik denklemlerin çözümlerinin patlaması

In this thesis, we study the problem of blow-up of solutions of second order nonlinear parabolic equations and numerical analysis of blow-up of solutions. Firstly, blow-up of solutions in semilinear heat equation is explained by using three methods namely concavity method, eigenfunction method and comparison method. Secondly, the finite difference approximation to the initial boundary value problem for semilinear heat equation is studied. Two convergence results are shown; the convergence of finite difference solution to the exact solution and the convergence of numerical blow-up time to the exact blow-up time.