A novelty Multi-Step Associated with Laplace Transform Semi Analytic Technique for Solving Generalized Non-linear Differential Equations

Abstract

In this work, a novel technique to obtain an accurate solutions to nonlinear form by multi-step combination with Laplace-variational approach (MSLVIM) is introduced. Compared with the traditional approach for variational it overcome all difficulties and enable to provide us more an accurate solutions with extended of the convergence region as well as covering to larger intervals which providing us a continuous representation of approximate analytic solution and it give more better information of the solution over the whole time interval. This technique is more easier for obtaining the general Lagrange multiplier with reduces the time and calculations. It converges rapidly to exact formula with simply computable terms with few time. To investigate of this technique, selected examples to show the ability, validity, accurately and effectiveness.

Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method

“…Many authors [21][22][23][24][25] have used higher order B-splines such as quintic, quartic, sextet and septic B-splines for the solutions of different PDEs but faced computational higher cost. Also, Riccati matrix delay differential equations has solved with variational iteration method in these papers [26][27][28][29][30].…”