Abstract
In this work, we solved the initial value problem of Benjamin−Bona−Mahony equation with generalized initial conditions by using differential transform method (DTM). We obtained the general solution in the form of a series. An example is presented for the particular initial conditions.
Highlights
Non-linear differential equations occurs in many areas of applied mathematics, engineering, physics and other sciences
Linear and nonlinear phenomenon occur in most of the recent fields of modern sciences and engineering. In such areas most of the problems are modeled by partial differential equations (PDEs)
Determining solutions of such partial differential equations has an important role in science problems
Summary
Non-linear differential equations occurs in many areas of applied mathematics, engineering, physics and other sciences. Linear and nonlinear phenomenon occur in most of the recent fields of modern sciences and engineering In such areas most of the problems are modeled by partial differential equations (PDEs). The main application of this technique was to solve both linear and nonlinear initial value problems in electrical circuit’s analysis In this method, transformation rules are applied to the differential equations and the initial or boundary conditions, the system are transformed into a set of algebraic equations in terms of the differential transforms of the original functions and the solution of these algebraic equations gives the desired solution of the problem. It gives exact values of the kth derivative of an analytical function at a point in terms of known and unknown boundary conditions in a fast manner It is a technique for the solutions of the differential equations in the form of polynomial series.
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