This paper concerns the study of the numerical approximation for the following initialboundary value problem{ut-uzx=f（u）,t∈（0,1）,t∈（0,T） u（0,t）=0,t∈（0,1）,t∈（0,T） u（x,0）=u0（x）,x∈（0,1）where f（s...This paper concerns the study of the numerical approximation for the following initialboundary value problem{ut-uzx=f（u）,t∈（0,1）,t∈（0,T） u（0,t）=0,t∈（0,1）,t∈（0,T） u（x,0）=u0（x）,x∈（0,1）where f（s） is a positive, increasing, C1 convex function for the nonnegative values of s, f（0） 〉0, f∞ds/f（s） 〈∞, u0∈C1（[0, 1]）, u0（0） = 0, u＇0（1）=0. We find some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiserete blow-up time. We also prove the convergence of the semidiscrete blow-up time to the theoretical one. A similar study has been also undertaken for a discrete form of the above problem. Finally, we give some numerical results to illustrate our analysis.展开更多
文摘This paper concerns the study of the numerical approximation for the following initialboundary value problem{ut-uzx=f（u）,t∈（0,1）,t∈（0,T） u（0,t）=0,t∈（0,1）,t∈（0,T） u（x,0）=u0（x）,x∈（0,1）where f（s） is a positive, increasing, C1 convex function for the nonnegative values of s, f（0） 〉0, f∞ds/f（s） 〈∞, u0∈C1（[0, 1]）, u0（0） = 0, u＇0（1）=0. We find some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiserete blow-up time. We also prove the convergence of the semidiscrete blow-up time to the theoretical one. A similar study has been also undertaken for a discrete form of the above problem. Finally, we give some numerical results to illustrate our analysis.
