Abstract:
Nonlinear phenomenon plays vital role in engineering and applied sciences. Higher order
nonlinear boundary value and initial value problems are known to describe a large variety
of phenomena. We are mainly concerned with finding the analytic solution of boundary
value and initial value problems of the type T ( u ) = 0, subject to some boundary and
initial conditions, where T is any differential or integral operator. We study and develop
some analytic methods for solving higher order nonlinear boundary value and initial
value problems. We propose several modifications in variation of parameters method for
finding the approximate solution of several higher order nonlinear boundary value, initial
value, parametric boundary value, higher dimensional and system of nonlinear Volterra
integro differential problems. We apply the exp-function method to construct generalized
soliton, travelling wave and periodic solution of several higher order nonlinear partial
differential equations. We apply the exp-function method for finding the exact solution of
some higher order nonlinear boundary value problems. All the suggested techniques are
compared with well known classical techniques and are found quite efficient, well suited
and reliable for the solution of higher order nonlinear boundary and initial value
problems of diversified nature.
