Block-Centered Difference Methods Of Two Classes For Evolution Equations

This article discussed hyperbolic equations and parabolic equations with the Crank -Nicolson block center finite di?erence method for all nonuniform grids. We not only canfind out the approximate solution and the approximate solution of the firstorder derivativeof solutions,but also get the discrete L2-norm errors of the approximate solution and su-per convergence estimateits of the approximate solution of the firstorder derivative of thesolutions.Firstly, we brie?y introduce the background of the paper and the studying problemconsidered.Scendly,We consider the Crank-Nicolson block-centered di?erence method for the so-lution of the linear parabolic di?erential problems in the bounded domain,with su?cientlysmooth data. We get the approximate solution and the approximate solution of thefirstorder derivative of solution for all nonuniform grids. In theory, we get the discreteL2-norm errors of the approximate solution and super convergence estimateits of the ap-proximate solution of the firstorder derivative of solutions. It is import that we get higherprecision in time.And this format is spreaded to the linear hyperbolic di?erential problems.Also we get the discrete L2-norm errors of the approximate solution and super convergenceestimateits of the approximate solution of the firstorder derivative of the solutions.Finally,two numerical examples are given,and their results are identical with theoret-ical analysis. These explain that the format has e?cient convergence.