Several Difference Schemes For The Damped Sine-Gordon Equation

Several unconditional stable difference schemes for the DampedSine-Gordon Equation is made in this dissertation. Three differenceschemes for the Damped Sine-Gordon Equation in one space dimension arestudied in chapter two with the truncation error O(τ~2 + h~2), the converg-ence and unconditional stability are obtained by the discrete functionsanalysis method. Numerical results shown that the scheme is effective anddependable.Two high order accurate compact difference schemes for the ab-ove equation are developed in chapter three ,which can get the truncationerror O(τ~2 + h~4) with less difference points, the convergence and unco-nditional stability are also obtained by the discrete functions analysismethod.In order to decrease the compute complexity of the equation intwo space dimensions, an alternating direction implicit method with itstruncation error O(τ~2 + h~2) is studied in chapter four.We introduce twoparameters γ1,γ2 ,and can get better numerical results through choose dif-ferent parameters with preserve its truncation error. At last ,we givethe numerical results of the scheme.