The Method Of Characteristic Block Centered Difference For Regularised Long Wave Equation

Regular long wave equation that it is called RLW equation, it is an important nonlinearwave equation in ?uid mechanics. Regularised Long Wave equation plays a major role in alarge number of partial di?erential equations. They can describe many important physicalphenomenons and equations, such as soliton theory, shallow water waves and ion acousticphasma waves and so on.First, a brief introduction is given to the latest development of these approaches. Thenwe introduce brie?y our work and the basic theory to be applied in this paper.Second, for the initial boundary value problem of RLW equation. The method ofcharacteristic block center di?erence for one-dimensional and two-dimensional linear reg-ularized long wave equation is given. The approximate solution of equation is obtained,we also get solution,s first order derivative and error estimation. The discrete L2 normmost optimal order number error estimation for approximate solution. The error order ofthe approximate solution is the same as one of the characteristic di?erence method basedon quadratic interpolation, and its first derivatives show super convergent. The first orderderivative approximate solution with approximate solution has the same accuracy.Finally, according to characteristic block center di?erence scheme of Regular long waveequation. The actual calculation example is given. The results show that the first orderderivative approximate solution with approximate solution has the same accuracy, and alsoshow that the method is e?ective and feasible.