Search results

This study aims to introduce a modern higher efficiency predictor–corrector iterative algorithm.

Furthermore, the efficiency of new algorithm is analyzed on the based on Chun-Hui He’s iteration method.

In comparison with the current robust algorithms, the newly establish algorithm behaves better and efficient, whereas the current existing algorithm fails or slows in the considered test examples.

The modified Chun-Hui He’s algorithm has great practical implication in numerous real-life challenges in different area of engineering, such as Industrial engineering, Civil engineering, Electrical engineering and Mechanical engineering.

The paper presents a modified Chun-Hui He’s algorithm for solving the nonlinear algebraic models exist in various area.

Every student knows Newton’s iteration method from a textbook, which is widely used in numerical simulation, what few may know is that its ancient Chinese partner, Ying Buzu Shu, in about second century BC has much advantages over Newton’s method. The purpose of this paper is to introduce the ancient Chinese algorithm and its modifications for numerical simulation.

An example is given to show that the ancient Chinese algorithm is insensitive to initial guess, while a fast convergence rate is predicted.

Two new algorithms, which are suitable for numerical simulation, are introduced by absorbing the advantages of the Newton iteration method and the ancient Chinese algorithm.

This paper focuses on a single algebraic equation; however, it is easy to extend the theory to algebraic systems.

The Newton iteration method can be updated in numerical simulation.

The ancient Chinese algorithm is elucidated to have modern applications in various numerical methods.

This study aims to purpose the idea of a new hybrid approach to examine the approximate solution of the fourth-order partial differential equations (PDEs) with time fractional derivative that governs the behaviour of a vibrating beam. The authors have also demonstrated the physical representations of the problem in different fractional order.

Mohand transform is a new technique that the authors use to reduce the order of fractional problems, and then the homotopy perturbation method can be used to handle the further series solution in the form of convergence. The formulation of Mohand transform and the homotopy perturbation method is known as Mohand homotopy perturbation transform (MHPT). The fractional order in this paper is considered in the Caputo sense.

The results are formulated in the shape of iterative series and predict the solution close to the exact solution. This successive iteration demonstrates the authenticity and reliability of this scheme.

This paper presents the significance of MHPT such that, firstly, Mohand transform is coupled with homotopy perturbation method and, secondly, the fractional order a is used to show the physical behaviour of the graphical solution.

This study presents the consistency and authenticity of the graphical solution with the exact solutions.

This study demonstrates that Mohand transform is capable to handle the fractional order problem without any constraints and assumptions.

A new integral transform has been introduced without any restriction of variables that produces the results in a series form and confirms the validity of the proposed algorithm by graphical illustrations.

The purpose of this paper is to introduce an innovative strategy for the approximate solution of the heat flow problems in two- and three-dimensional spaces. This new strategy is very easy to implement and handles the restrictive variable that may ruin the physical nature of the problem.

This study combines Sawi transform (ST) and the homotopy perturbation method (HPM) to formulate the idea of Sawi homotopy perturbation transform method (SHPTM). First, this study implements ST to handle the recurrence relation and then incorporates HPM to derive the series solutions of this recurrence relation. ST has the advantage in that it does not require any assumptions or hypothesis for the evaluation of series solutions.

This strategy finds the results very accurate and close to the precise solution. The graphical observations and the surface solution demonstrate that SHPTM is a reliable and powerful scheme for finding the approximate solution of heat flow problems.

The study presents an original work. This study develops SHPTM for the approximate solution of two- and three-dimensional heat flow problems. The obtained results and graphical representation demonstrate that SHPTM is a very authentic and reliable approach.