We deal with an inverse problem of simultaneously identifying the space-dependent diffusion coefficient and the source magnitude in the time fractional diffusion equation from viewpoint of numerics. Such simultaneous inversion problem is often of severe ill-posedness as compared with that of determining a single coefficient function. The forward problem is solved by employing an implicit finite...

Abstract We analyse numerically the periodic problem and initial boundary value of Korteweg-de Vries equation Drindfeld–Sokolov–Wilson using summation-by-parts simultaneous-approximation-term method. Two sets conditions are derived for each which stability is shown energy Numerical analysis done when solution interacts with boundaries. Results show benefit higher order SBP operators.

Abstract This paper proposes a denoising algorithm for physical, electronic images based on fractional differential equations. The effectively combines calculus theory and gradient descent flow. At the same time, we introduce time factor into improved model spatial partial equation. We take advantage of unique amplitude-frequency characteristic operation to preserve texture details with little ...

reduced differental transform method (rdtm), which isone of the useful and effective numerical method, is applied to solve nonlinear time-dependent foam drainage equation (fde) with different initial conditions. we compare our method with the famous adomian decomposition and laplace decomposition methods. the obtained resultsdemonstrated that rdtm is a powerful tool for solving nonlinear par...

in this paper, nonlinear klein-gordon equation with quadratic term is solved by means of an analytic technique, namely the homotopy analysis method (ham).comparisons are made between the adomian decomposition method (adm), the exact solution and homotopy analysis method. the results reveal that the proposed method is very effective and simple.