Advances in the Solution of Nonlinear Differential Equations [Working Title]最新文献

Boundary Element Method for the Mixed BBM-KdV Equation Compared to Non Standard Boundary Conditions 混合BBM-KdV方程的边界元法与非标准边界条件的比较

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-06-04 DOI: 10.5772/INTECHOPEN.96617

M. Abounouh, H. Al-Moatassime, S. Kaouri, Y. Ouakrim

引用次数: 0

On Some Important Ordinary Differential Equations of Dynamic Economics 关于动态经济学的几个重要常微分方程

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-04-21 DOI: 10.5772/INTECHOPEN.97130

Anastasios Tsoularis

{"title":"On Some Important Ordinary Differential Equations of Dynamic Economics","authors":"Anastasios Tsoularis","doi":"10.5772/INTECHOPEN.97130","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.97130","url":null,"abstract":"Mathematical modeling in economics became central to economic theory during the decade of the Second World War. The leading figure in that period was Paul Anthony Samuelson whose 1947 book, Foundations of Economic Analysis, formalized the problem of dynamic analysis in economics. In this brief chapter some seminal applications of differential equations in economic growth, capital and business trade cycles are outlined in deterministic setting. Chaos and bifurcations in economic dynamics are not considered. Explicit analytical solutions are presented only in relatively straightforward cases and in more complicated cases a path to the solution is outlined. Differential equations in modern dynamic economic modeling are extensions and modifications of these classical works. Finally we would like to stress that the differential equations presented in this chapter are of the “stand-alone” type in that they were solely introduced to model economic growth and trade cycles. Partial differential equations such as those which arise in related fields, like Bioeconomics and Differential Games, from optimizing the Hamiltonian of the problem, and stochastic differential equations of Finance and Macroeconomics are not considered here.","PeriodicalId":279002,"journal":{"name":"Advances in the Solution of Nonlinear Differential Equations [Working Title]","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130494738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Boundary Element Modeling and Simulation Algorithm for Fractional Bio-Thermomechanical Problems of Anisotropic Soft Tissues 各向异性软组织分式生物热力学问题的边界元建模与仿真算法

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-04-05 DOI: 10.5772/INTECHOPEN.96268

M. Fahmy

引用次数: 3

The Uniformly Parabolic Equations of Higher Order with Discontinuous Data in Generalized Morrey Spaces and Elliptic Equations in Unbounded Domains 广义Morrey空间中具有不连续数据的高阶一致抛物方程和无界区域上的椭圆方程

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-03-22 DOI: 10.5772/INTECHOPEN.96781

T. Gadjiev, Konul G. Suleymanova

引用次数: 0

Using the Boundary Element Method to Simulate Visco-Elastic Deformations of Rough Fractures 用边界元法模拟粗糙断口粘弹性变形

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-02-25 DOI: 10.5772/INTECHOPEN.96229

Hao Kang

{"title":"Using the Boundary Element Method to Simulate Visco-Elastic Deformations of Rough Fractures","authors":"Hao Kang","doi":"10.5772/INTECHOPEN.96229","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.96229","url":null,"abstract":"In many engineering applications, such as tribology and rock mechanics, it is very important to understand the deformation of rough fractures to evaluate the safety and profitability of the project. Since a lot of materials can be characterized as visco-elastic materials, it is very significant to simulate the visco-elastic deformation of rough fractures. This chapter focuses on using the boundary element method to simulate visco-elastic deformations of rough fractures. First, the principles and procedures of the above-mentioned method will be introduced. Then, one example will be given in detail. This example investigates the effect of surface geometry on visco-elastic deformations of rough rock fractures under normal compressive stresses. The rock fracture surfaces are assumed to be self-affine, and synthetic rough surfaces are generated by systematically changing three surface roughness parameters: the Hurst exponent, root mean square roughness, and mismatch length. The results indicate that by decreasing the Hurst exponent or increasing the root mean square roughness or increasing the mismatch length, the fracture mean aperture increases, and the contact ratio (the number of contacting cells/total number of cells) increases slower with time. Finally, the limitations and possible future research directions will be briefly discussed.","PeriodicalId":279002,"journal":{"name":"Advances in the Solution of Nonlinear Differential Equations [Working Title]","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130370671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Solution of Nonlinear Partial Differential Equations by Mixture Adomian Decomposition Method and Sumudu Transform 用混合Adomian分解法和Sumudu变换求解非线性偏微分方程

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-01-12 DOI: 10.5772/INTECHOPEN.94598

T. Elzaki, Shams E. Ahmed

引用次数: 1

Solving Second-Order Differential Equations by Decomposition 用分解法求解二阶微分方程

Advances in the Solution of Nonlinear Differential Equations [Working Title] Pub Date : 2021-01-04 DOI: 10.5772/INTECHOPEN.94993

F. Schwarz

引用次数: 0