On the Finite Differences Method Using Microsoft Excel | Chapter 9 | Research Highlights in Mathematics and Computer Science Vol. 6

 In mathematical analysis, finite-dissimilarity methods (FDM) are a class of mathematical techniques for solving characteristic equations by approximating derivatives accompanying finite dissimilarities. Both the spatial domain and opportunity interval (if applicable) are discretized, or defective into a finite number of steps, and the advantage of the solution at these discrete points is approximated by answering algebraic equatings containing finite distinctnesses and values from nearby points. Finite difference procedures convert ordinary characteristic equations (ODE) or partial characteristic equations (PDE), which grant permission be nonlinear, into a system of uninterrupted equations that can be resolved by matrix algebra methods. Modern computers can act these linear algebra computations capably which, along with their relative ease of exercise, has led to the extensive use of FDM in modern numerical study. Today, FDMs are one of the most prevalent approaches to solving PDEs, in addition to finite element patterns. This paper suggests a solution by construction up a library of solvers utilizing spreadsheets, with the effect that the encapsulated information of building modelling solvers can later be secondhand for education or certain-world problems. This study raises concern about the epitomized body of knowledge that has donated to the emergence and the establishment of displaying software applications because 1980. This body of knowledge encompasses a deep understanding of differential equations that illustrate physical problems and their mathematical transformation into plans of linear equations.

Author(s) Details:

Farzin Salmasi,
Department of Water Engineering, Faculty of Agriculture, University of Tabriz, Tabriz, Iran.

John Abraham,
School of Engineering, University of St. Thomas, 2115 Summit Avenue St. Paul, Minnesota-55105, USA.

Please see the link here: https://stm.bookpi.org/RHMCS-V6/article/view/9804

On the Finite Differences Method Using Microsoft Excel | Chapter 11 | Research Highlights in Mathematics and Computer Science Vol. 6

 In mathematical analysis, finite-distinctness methods (FDM) are a class of mathematical techniques for solving characteristic equations by approximating derivatives accompanying finite distinctnesses. Both the spatial domain and opportunity interval (if applicable) are discretized, or defective into a finite number of steps, and the worth of the solution at these discrete points is approximated by answering algebraic equatings containing finite distinctnesses and values from nearby points. Finite difference systems convert ordinary characteristic equations (ODE) or partial characteristic equations (PDE), which concede possibility be nonlinear, into a system of uninterrupted equations that can be answered by matrix algebra methods. Modern computers can act these linear algebra computations capably which, along with their relative ease of exercise, has led to the extensive use of FDM in modern numerical study. Today, FDMs are one of the most accepted approaches to solving PDEs, in addition to finite element procedures. This paper suggests a solution by construction up a library of solvers utilizing spreadsheets, with the effect that the encapsulated information of building modelling solvers can later be secondhand for education or actual-world problems. This study raises concern about the epitomized body of knowledge that has donated to the emergence and the establishment of displaying software applications because 1980. This body of knowledge composes a deep understanding of differential equations that characterize physical problems and their mathematical transformation into structures of linear equations.

Author(s) Details:

Farzin Salmasi,
Department of Environmental Health, Dian Nuswantoro University Semarang, Indonesia.

John Abraham,
School of Engineering, University of St. Thomas, 2115 Summit Avenue St. Paul, Minnesota-55105, USA.

Please see the link here: https://stm.bookpi.org/RDASS-V6/article/view/7860

Analysis of Methods for Calculating the Value of the Thermal Conductivity Coefficient in Numerical Modeling | Chapter 07 | Novel Research Aspects in Mathematical and Computer Science Vol. 3

 Using the method of computational experiments on a computer, the effect of the method for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid on the numerical solutions of a one-dimensional nonlinear problem of heat conduction according to explicit and implicit conservative difference schemes is investigated in this article. Thermal conductivity has a power-law relationship with temperature. It is demonstrated that the technique for determining the values of the thermal conductivity coefficient at the nodes of the difference grid affects the accuracy of numerical solutions derived by both the explicit and implicit difference schemes. A approach is suggested for obtaining a numerical solution that is sufficiently near to the analytical solution.

Author(S) Details

Z. U. Uzakov
Karshi Branch of Tashkent University of Information Technologies Named After Muhammad al-Khorazmi, 180002 Karshi, Beshkent highway, 3d Kilometer, Uzbekistan.

View Book:- https://stm.bookpi.org/NRAMCS-V3/article/view/6814