Efficient Iterative Method for Solving Korteweg-de Vries Equations
The Korteweg-de Vries equation plays an important role in fluid physics andÂ applied mathematics. This equation is a fundamental within study of shallow waterÂ waves. Since these equations arise in many applications and physical phenomena, itÂ is officially showed that this equation has solitary waves as solutions, TheÂ Korteweg-de Vries equation is utilized to characterize a long waves travelling inÂ channels. The goal of this paper is to construct the new effective frequent relation toÂ resolve these problems where the semi analytic iterative technique presents newÂ enforcement to solve Korteweg-de Vries equations. The distinctive feature of thisÂ method is, it can be utilized to get approximate solutions for travelling waves ofÂ non-linear partial differential equations with small amount of computations does notÂ require to calculate restrictive assumptions or transformation like other conventionalÂ methods. In addition, several examples clarify the relevant features of this presentedÂ method, so the results of this study are debated to show that this method is aÂ powerful tool and promising to illustrate the accuracy and efficiency for solvingÂ these problems. To evaluate the results in the iterative process we used the MatlabÂ symbolic manipulator.