Mathematical and Computational Applications

434 KiB

Open AccessArticle

Solution of Quadratic Nonlinear Problems with Multiple Scales Lindstedt-Poincare Method

by Mehmet Pakdemirli and Gözde Sarı

Math. Comput. Appl. 2015, 20(2), 137-150; https://doi.org/10.3390/mca20010150 - 01 Aug 2015

Cited by 1 | Viewed by 1331

A recently developed perturbation algorithm namely the multiple scales Lindstedt-Poincare method (MSLP) is employed to solve the mathematical models. Three different models with quadratic nonlinearities are considered. Approximate solutions are obtained with classical multiple scales method (MS) and the MSLP method and they [...] Read more.

A recently developed perturbation algorithm namely the multiple scales Lindstedt-Poincare method (MSLP) is employed to solve the mathematical models. Three different models with quadratic nonlinearities are considered. Approximate solutions are obtained with classical multiple scales method (MS) and the MSLP method and they are compared with the numerical solutions. It is shown that MSLP solutions are better than the MS solutions for the strongly nonlinear case of the considered models. Full article

735 KiB

Open AccessArticle

Co-Evolution Analysis on Coal-Power Industries Cluster Ecosystem Based on the Lotka-Volterra Model: A Case Study of China

by Cui Herui, Peng Xu and Zhao Yuqi

Math. Comput. Appl. 2015, 20(2), 121-136; https://doi.org/10.3390/mca20010136 - 01 Aug 2015

Cited by 1 | Viewed by 1447

Abstract

This contradiction caused by differences in coal-electricity industry market forces is “market for coal, plans for electricity". The traditional coal and power enterprises cause serious pollution problems and ecological problems in the production process, restricting the sustainable socio-economic development. The coal-electricity industry cluster [...] Read more.

This contradiction caused by differences in coal-electricity industry market forces is “market for coal, plans for electricity". The traditional coal and power enterprises cause serious pollution problems and ecological problems in the production process, restricting the sustainable socio-economic development. The coal-electricity industry cluster ecosystem forms may effectively mediate organizations conflict existing in the development of industrial clusters, improving resource utilization, reducing energy consumption, to achieve harmony with the natural environment. This paper combines with the theory of industrial ecology, with the Lotka-Volterra model, to explore co-evolution mechanism of coal–electricity industry cluster at the micro, meso and macro levels. In the end, this paper adapted the "Henon mapping" method to describe the chaos phenomenon existed in the development. This paper put forward specific development model for industrial clusters in lower, steady and advanced stages. The co-evolution coal-electricity industry cluster ecosystem is a good solution to numerous conflicts. Full article

727 KiB

Open AccessArticle

Visual and Computational Comparison of Functionals Used in Density Functional Theory

by K. M. Flurchick

Math. Comput. Appl. 2015, 20(2), 111-120; https://doi.org/10.3390/mca20010120 - 01 Aug 2015

Viewed by 1214

Abstract

This work presents the visual and quantitative comparison of Density Functional Theory (DFT) exchange-correlation energy E_xc functionals with Coupled Cluster with Single and Double excitations (CCSD) calculations (and experiment where possible). The E_xc functional is an approximate term which is a [...] Read more.

This work presents the visual and quantitative comparison of Density Functional Theory (DFT) exchange-correlation energy E_xc functionals with Coupled Cluster with Single and Double excitations (CCSD) calculations (and experiment where possible). The E_xc functional is an approximate term which is a component of the total energy of a molecule. This comparison is based on visualizing the differences of computed properties, such as the charge density, geometry and other molecular properties between the functional and a CCSD calculation. In this work, this visual comparison for a set of functionals using a set of small molecules is presented to elucidate the method. Specifically, this visual comparison of the local molecular properties includes the charge density and electron localization function and global molecular properties such as molecular geometry for each DFT functional compared with a CCSD calculation. Note, that the differences of the particular computed properties are computed visually. Full article

249 KiB

Open AccessArticle

A Weakly Convergence Result on Lp(x) Spaces

by Yasin Kaya

Math. Comput. Appl. 2015, 20(2), 106-110; https://doi.org/10.3390/mca20010110 - 01 Aug 2015

Viewed by 1693

Abstract

In this paper with 1 < p^-≤ p⁺ <∞ condition we prove a weak convergence result under pointwise convergence and bounded of the sequence. Our theorem is an extension of classical result to variable exponent setting. Full article

523 KiB

Open AccessArticle

Fermat Collocation Method for Nonlinear System of First Order Boundary Value Problems

by Dilek Taştekin and Salih Yalçınbaş

Math. Comput. Appl. 2015, 20(2), 94-105; https://doi.org/10.3390/mca20010105 - 01 Aug 2015

Viewed by 1157

Abstract

In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of first order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we [...] Read more.

In this study, a numerical approach is proposed to obtain approximate solutions of nonlinear system of first order boundary value problem. This technique is essentially based on the truncated Fermat series and its matrix representations with collocation points. Using the matrix method, we reduce the problem to a system of nonlinear algebraic equations. Numerical examples are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and produces accurate results. Full article

1026 KiB

Open AccessArticle

Shifted Jacobi Collocation Method Based on Operational Matrix for Solving the Systems of Fredholm and Volterra Integral Equations

by Abdollah Borhanifar and Khadijeh Sadri

Math. Comput. Appl. 2015, 20(2), 76-93; https://doi.org/10.3390/mca20010093 - 01 Aug 2015

Cited by 1 | Viewed by 1549

Abstract

This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product. The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra equations. These matrices together [...] Read more.

This paper aims to construct a general formulation for the shifted Jacobi operational matrices of integration and product. The main aim is to generalize the Jacobi integral and product operational matrices to the solving system of Fredholm and Volterra equations. These matrices together with the collocation method are applied to reduce the solution of these problems to the solution of a system of algebraic equations. The method is applied to solve system of linear and nonlinear Fredholm and Volterra equations. Illustrative examples are included to demonstrate the validity and efficiency of the presented method. Also, several theorems, which are related to the convergence of the proposed method, will be presented. Full article

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Math. Comput. Appl., Volume 20, Issue 2 (August 2015) – 6 articles , Pages 76-150

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