Ch. Srinivasa Rao

Abstract: In this paper, we construct large-time asymptotic solution of the modified Burgers equation with sinusoidal initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study.

Abstract: The modified Burgers equation u t + u n u x = δu xx 2 , where n ≥ 2 is even, is treated analytically for N-wave initial conditions. An exact asymptotic solution is presented, extending the validity of the linear solution far back in time.

Abstract: The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming certain asymptotic conditions at plus infinity or minus infinity, we find a wide variety of solutions(positive) single hump, monotonic (bounded or unbounded) or solutions with a finite zero. The existence or non-existence of positive bounded solutions with exponential decay to zero at infinity for specific parameter ranges is proved. The analysis relies mainly on the shooting argument.

Abstract: In this paper, we construct large-time asymptotic solutions of some generalized Burgers equations with periodic initial conditions by using a balancing argument. These asymptotics are validated by a careful numerical study. We also show that our asymptotic results agree with the approximate solutions obtained by Parker [1] in certain limits.

Abstract: The fractional partial differential equations stand for natural phenomena all over the world from science to engineering. When it comes to obtaining the solutions of these equations, there are many various techniques in the literature. Some of these give to us approximate solutions; others give to us analytical solutions. In this paper, we applied the modified trial equation method (MTEM) to the one-dimensional nonlinear fractional wave equation (FWE) and time fractional generalized Burgers equation. Then, we submitted 3D graphics for different value of .

Abstract: Presents simple analytic methods which are readily accessible for use in applications. These include transformations, phase plane analysis, integral equation formulation, shooting arguments, local and asymptotic analysis, singular point analysis, and others. The applications, reflecting the research

Abstract: In this paper, we investigate the numerical solutions of one dimensional modified Burgers’ equation with the help of Haar wavelet method. In the solution process, the time derivative is discretized by finite difference, the nonlinear term is linearized by a linearization technique and the spatial discretization is made by Haar wavelets. The proposed method has been tested by three test problems. The obtained numerical results are compared with the exact ones and those already exist in the literature. Also, the calculated numerical solutions are drawn graphically. Computer simulations show that the presented method is computationally cheap, fast, reliable and quite good even in the case of small number of grid points.

Abstract: A finite-difference scheme based on fourth-order rational approximants to the matrix-exponential term in a two-time level recurrence relation is proposed for the numerical solution of the modified Burgers equation. The resulting nonlinear system, which is analyzed for stability, is solved using an already known modified predictor-corrector scheme. The results arising from the experiments are compared with the corresponding ones known from the available literature.