Skema Berangka Untuk Masalah Goursat

Masalah Goursat merupakan masalah matematik yang melibatkan persamaan pembezaan separa yang mempunyai terbitan bercampur. la ditemui di dalam banyak bidang sains dan teknologi. Beberapa kajian berangka khususnya kaedah beza terhingga telah dilakukan dari pelbagai sudut oleh penyelidik terdahulu berkaitan dengan masalah ini. Di antara skema yang telah dibangunkan terdapat skema yang mengimplimentasi pengiraan menggunakan min harmonik nilai fungsi untuk menyelesaikan masalah Goursat dan keputusan daripada suatu kajian perbandingan yang telah dijalankan mendapati peningkatan tahap kejituan apabila pengiraan menggunakan min harmonik berbanding min geometrik dan min aritmetik. Justeru itu kajian tersebut menegaskan bahawa tahap kejituan sesuatu skema dipengaruhi sesuatu min yang dipilih. Walaubagaimanapun kajian lain telah menunjukkan secara berangka penggunaan rnin aritmetik memberikan penyelesaian lebih jitu berbanding min harmonik

Numerical Solution Of A Linear Goursat Problem Stability,Consistency And Convergence .

The Goursat problem, associated with hyperbolic partial differential equations, arises in several areas of applications. These include mathematical modeling of reacting gas flows and supersonic flow

Numerical Solution Of The Goursat Problem.

The Goursat problem, associated with hyperbolic partial differential equations, arises in several areas of applications. Several finite difference schemes have been proposed to solve the Goursat problem

A fourth-order compact finite difference scheme for the Goursat problem

A high-order uniform Cartesian grid compact finite difference scheme for the Goursat problem is developed. The basic idea of high-order compact schemes is to find the compact approximations to the derivatives terms by differentiating centrally the governing equations. Our compact scheme will approximate the derivative terms by involving the higher terms and reducing the number of grid points. The compact finite difference scheme is given for general form of the Goursat problem in uniform domain and illustrates the performance by applying a linear problem. Numerical experiments have been conducted with the new scheme and encouraging results have been obtained. In this paper we present the compact finite difference scheme for the Goursat problem. With the aid of computational software the scheme was programmed for determining the relative errors of linear Goursat problem

Steady Thermosolutocapillary Instability in Fluid Layer with Nondeformable Free Surface in the Presence of Insoluble Surfactant and Gravity

Steady thermosolutocapillary instabilities in a horizontal thin fluid layer with deformable free surface and uniform temperature at the bottom boundary in the presence of insoluble surfactant and gravity force are examined. The surface tension at the free surface is assumed to be linearly dependent on temperature and concentration gradients. The linear stability theory and the Galerkin method are used to obtain the closed form solutions. The effects of the controlling parameters, namely the Rayleigh number, Biot number, Lewis number, and elasticity parameter on the onset of Marangoni convection are analyzed. The results show that the gravitational force acts as destabilizer while the presence of surfactant delays the onset of convection

A new three-term conjugate gradient method with application to regression analysis

Conjugate gradient (CG) method is well-known for its ability to solve unconstrained optimization (UO) problem. This article presents a new CG method with sufficient descent condition that improves the Rivaie, Mustafa, Ismail and Leong (RMIL) method. The proposed method’s efficacy has been demonstrated through simulations on the Kijang Emas pricing regression problem. The daily data is obtained from Malaysian Ministry of Health and Bank Negara Malaysia between January 2021 and May 2021. The dependent variable for this study is the Kijang Emas price, and the independent variables are the coronavirus disease (COVID-19) measures (i.e., new cases, R-naught, death cases, new recovered). Data collected are analyzed on its correlation and coefficient determinant, and the influence of the COVID-19 on the Kijang Emas price is examined through the multiple linear regression model. The findings reveal that the suggested technique outperforms existing CG algorithms in terms of computing efficiency