The purpose of this paper is to employ the Adomian Decomposition Method (ADM) and
Restarted Adomian Decomposition Method (RADM) with new useful techniques to resolve …

In this paper, a new technique of homotopy analysis method (nHAM) is proposed for solving
second order nonlinear differential equations. This method improves the convergence of the …

In this paper, we develop a higher order numerical method for the fractional Bagley‐Torvik
equation. The main tools used include a new fourth‐order approximation for the fractional …

The wavelet multiresolution interpolation for continuous functions defined on a finite interval
is developed in this study by using a simple alternative of transformation matrix. The wavelet …

In This paper, we present analytic approximate solutions for Bratu's problem with high
accuracy for different values of λ. We solve this nonlinear problem without any …

The article introduces a new multistage technique for solving a polynomial system of
nonlinear initial and boundary value problems of differential equations. The radius of …

In this article, we illustrate how the Adomian polynomials can be utilized with different types
of iterative series solution methods for nonlinear equations. Two methods are considered …

In this paper, the reproducing kernel Hilbert space method (RKHSM) is applied for solving
Troesch's problem. We used numerical examples to illustrate the accuracy and …

This work presents a direct procedure to apply Padé method to find approximate solutions
for nonlinear differential equations. Moreover, we present some cases study showing the …

We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu
problems. Chebyshev wavelets expansions together with operational matrix of derivative are …