A Survey of Regularization Methods for First-Kind Volterra Equations

2000 ◽  
pp. 53-82 ◽  
Author(s):  
Patricia K. Lamm
Keyword(s):  
Volterra Equations ◽  
Regularization Methods

Modeling the co-evolution of economic institutions and the economy of resource producing regions

2020 ◽  
Vol 18 (4) ◽  
pp. 122-131
Author(s):  
Vadim F. Islamutdinov ◽  
Sergey P. Semenov
Keyword(s):  
Economic Growth ◽  
Resource Availability ◽  
Regional Economy ◽  
Cumulative Effect ◽  
Volterra Equations ◽  
Economic Institutions ◽  
Predator Prey Model ◽  
Resource Endowment ◽  
Disincentive Effect ◽  
Good Institution

The purpose of the study is to develop a model for the co-evolution of the regional economy and economic institutions. The research methods used: abstract-logical for the study of theoretical aspects and the experience of modeling co-evolution; and economic-mathematical for the development of own model of coevolution. The results of the study: approaches to modeling the evolution of economic institutions, as well as the co-evolution of the regional economy and economic institutions are considered, strengths and weaknesses of existing approaches to modeling co-evolution are identified, on the basis of the logistic model and Lotka-Volterra equations, an own co-evolution model has been developed, which includes three entities: regional economy, “good” institution and “bad” institution. Three versions of the model have been developed: the co-evolution of the regional economy and the “good” institution, the co-evolution of the regional economy and the “bad institution,” and a variant of the co-evolution of all three entities simultaneously, in which the “good” and “bad” institutions interact according to the “predator-prey” model, and their the cumulative effect determines the development of the regional economy. Numerical experiments have been carried out in the MathLab, which have shown the capabilities of the model to reflect the results of the co-evolution of the economy of a resource-producing region and economic institutions. In the first variant, a “good” institution promotes economic growth in excess of the level determined by resource availability. In the second variant, the “bad” institution has a disincentive effect on the GRP, as a result of which the GRP falls below the level determined by the resource endowment. In the third variant, the interaction of “good” and “bad” institutions still contributes to economic growth above the level determined by resource availability, but causes cyclical fluctuations in the GRP.

Comparisons of regularization methods and regularization parameter selection methods in sound source identification using inverse boundary element method

2019 ◽  
Vol 67 (3) ◽  
pp. 219-227
Author(s):  
Youhong Xiao ◽  
Qingqing Song ◽  
Shaowei Li ◽  
Guoxue Lv ◽  
Zhenlin Ji
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Transfer Matrix ◽  
Sound Source ◽  
Source Identification ◽  
Regularization Parameter ◽  
Vibration Velocity ◽  
Regularization Methods ◽  
Inverse Boundary ◽  
Element Method

In noise source identification based on the inverse boundary element method (IBEM), the boundary vibration velocity is predicted based on the field pressure through a transfer matrix of the vibration velocity and field pressure established on the Helmholtz integral equation. Because the matrix is often ill-posed, it needs to be regularized before reconstructing the vibration velocity. Two regularization methods and two methods of selecting the regularization parameter are investigated through the simulation analysis of a pulsating sphere. The result of transfer matrix regularization is further verified through the reconstruction of the vibration of an aluminum plate. Additionally, to reduce the large errors at some frequencies in the reconstruction result, increasing the number of measuring points is more effective than reducing the distance between the measurement plane and the sound source.

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

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