A Meshfree Numerical Technique Based on Radial Basis Function Pseudospectral Method for Fisher’s Equation

2020 ◽  
Vol 21 (1) ◽  
pp. 37-49
Author(s):  
Geeta Arora ◽  
Gurpreet Singh Bhatia
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Technique ◽  
Pseudospectral Method ◽  
Numerical Results ◽  
Fisher’S Equation ◽  
Optimal Value ◽  
Radial Basis ◽  
Fisher's Equation ◽  
Leave One Out

AbstractThis paper concerns with the implementation of radial basis function pseudospectral (RBF-PS) method for solving Fisher’s equation. Pseudospectral methods are well known for being highly accurate but are limited in terms of geometric flexibility. Radial basis function (RBF) in combination with the pseudospectral method is capable to overcome this limitation. Using RBF, Fisher’s equation is approximated by transforming it into a system of ordinary differential equations (ODEs). An ODE solver is used to solve the resultant ODEs. In this approach, the optimal value of the shape parameter is discussed with the help of leave-one out cross validation strategy which plays an important role in the accuracy of the result. Several examples are given to demonstrate the accuracy and efficiency of the method. RBF-PS method is applied using different types of basis functions and a comparison is done based upon the numerical results. A two-dimensional problem that generalizes the Fisher’s equation is also solved numerically. The obtained numerical results and comparisons confirm that the use of RBF in pseudospectral mode is in good agreement with already known results in the literature.

scholarly journals Radial Basis Function Pseudospectral Method for Solving Standard Fitzhugh-Nagumo Equation

2020 ◽  
Vol 5 (6) ◽  
pp. 1488-1497
Author(s):  
Geeta Arora ◽  
Gurpreet Singh Bhatia
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Shape Parameter ◽  
Cross Validation ◽  
Pseudospectral Method ◽  
Mesh Free ◽  
Radial Basis ◽  
Nagumo Equation ◽  
The Stability ◽  
Leave One Out

In this article, a pseudospectral approach based on radial basis functions is considered for the solution of the standard Fitzhugh-Nagumo equation. The proposed radial basis function pseudospectral approach is truly mesh free. The standard Fitzhugh-Nagumo equation is approximated into ordinary differential equations with the help of radial kernels. An ODE solver is applied to solve the resultant ODEs. Shape parameter which decides the shape of the radial basis function plays a significant role in the solution. A cross-validation technique which is the extension of the statistical approach leave-one-out-cross-validation is used to find the shape parameter value. The presented method is demonstrated with the help of numerical results which shows a good understanding with the exact solution. The stability of the proposed method is demonstrated with the help of the eigenvalues method numerically.

scholarly journals Classificação do Risco de Quedas em Idosos com Least Squares Support Vector Regression Utilizando Sinais Eletromiográficos e Dinamométricos

2021 ◽  
Author(s):  
Daniele Alves Silva ◽  
Laiana Sepúlveda de Andrade Mesquita ◽  
Luan Marinho Morais Pereira ◽  
Nayra Ferreira Lima Castelo Branco ◽  
Hermes Manoel Galvão Castelo Branco ◽  
...  
Keyword(s):  
Radial Basis Function ◽  
Least Squares ◽  
Support Vector Regression ◽  
Basis Function ◽  
Support Vector ◽  
Radial Basis ◽  
Leave One Out

A determinação do risco de cair é de suma importância na assistência à saúde do idoso, pois a ocorrência de quedas nessa população trazem consequências em vários aspectos. Ferramentas de aprendizado de máquinas têm sido cada vez mais empregadas com este fim. Portanto, o objetivo deste estudo foi investigar a viabilidade da utilização de sinais eletromiográficos e dinamométricos na classificação do risco de quedas em idosos via modelo least squares support vector regression (LSSVR). Trinta e um voluntários idosos foram avaliados com a Escala de Equilíbrio de Berg (EEB), eletromiografia e dinamometria do membro inferior dominante. Para o modelo LSSVR foram utilizados kernels do tipo linear, polinomial e radial basis function (RBF), além de validações cruzadas pelos métodos leave one out e K-fold. Ambos os sinais apresentaram erros médios baixos na maioria das execuções realizadas. Dessa forma, verificou-se que é possível classificar o risco de quedas em idosos por meio de sinais eletromiográficos e dinamométricos aplicados ao modelo LSSVR.

Buckling of Laminated Composite and Sandwich Plates Using Radial Basis Function Collocations

2015 ◽  
Vol 15 (01) ◽  
pp. 1540002 ◽  
Author(s):  
Sandeep Singh ◽  
Jeeoot Singh ◽  
Karunesh Kumar Shula
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Present Method ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Composite Plates ◽  
Sandwich Plates ◽  
Finite Point ◽  
Optimal Value ◽  
Radial Basis

In this paper, buckling analysis of isotropic, orthotropic, laminated composite and sandwich plates utilizing trigonometric shear deformation theory and meshless method based on the finite point formulation using thin plate, polynomial and inverse multiquadric radial basis function is presented. The convergence of the present method is studied for isotropic and laminated composite plates for different radial basis functions with optimal value of shape parameter. Numerical examples of laminated and sandwich plates subjected to various types of in-plane loads are solved to demonstrate accuracy and applicability of present method. Several new results for variety of composite and sandwich plates are presented. The present results are observed to be in good agreement with those available in literature. The effects of orthotropy ratio of material, span to thickness ratio, number of layers, core thickness and lamination scheme on the critical load of plates are also presented.

A radial basis function network classifier to maximise leave-one-out mutual information

2014 ◽  
Vol 23 ◽  
pp. 9-18 ◽  
Author(s):  
Xia Hong ◽  
Sheng Chen ◽  
Abdulrohman Qatawneh ◽  
Khaled Daqrouq ◽  
Muntasir Sheikh ◽  
...  
Keyword(s):  
Mutual Information ◽  
Radial Basis Function ◽  
Basis Function ◽  
Radial Basis Function Network ◽  
Radial Basis ◽  
Leave One Out ◽  
Function Network

scholarly journals Adaptive Radial Basis Function Partition of Unity Interpolation: A Bivariate Algorithm for Unstructured Data

2021 ◽  
Vol 87 (2) ◽  
Author(s):  
Roberto Cavoretto
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Adaptive Algorithm ◽  
Likelihood Estimation ◽  
Partition Of Unity ◽  
Adaptive Method ◽  
Scattered Data ◽  
Radial Basis ◽  
Square Cells ◽  
Leave One Out

AbstractIn this article we present a new adaptive algorithm for solving 2D interpolation problems of large scattered data sets through the radial basis function partition of unity method. Unlike other time-consuming schemes this adaptive method is able to efficiently deal with scattered data points with highly varying density in the domain. This target is obtained by decomposing the underlying domain in subdomains of variable size so as to guarantee a suitable number of points within each of them. The localization of such points is done by means of an efficient search procedure that depends on a partition of the domain in square cells. For each subdomain the adaptive process identifies a predefined neighborhood consisting of one or more levels of neighboring cells, which allows us to quickly find all the subdomain points. The algorithm is further devised for an optimal selection of the local shape parameters associated with radial basis function interpolants via leave-one-out cross validation and maximum likelihood estimation techniques. Numerical experiments show good performance of this adaptive algorithm on some test examples with different data distributions. The efficacy of our interpolation scheme is also pointed out by solving real world applications.

scholarly journals Radial Basis Function in Nonlinear Black-Scholes Option Pricing Equation with Transaction Cost

2019 ◽  
pp. 1-11
Author(s):  
Godwin Onwona-Agyeman ◽  
Francis T. Oduro
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Technique ◽  
Option Price ◽  
Meshfree Approximation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
The World ◽  
Radial Basis

Differential equations play significant role in the world of finance since most problems in these areas are modeled by differential equations. Majority of these problems are sometimes nonlinear and are normally solved by the use of numerical methods. This work takes a critical look at Nonlinear Black-Scholes model with special reference to the model by Guy Barles and Halil Mete Soner. The resulting model is a nonlinear Black-Scholes equation in which the variable volatility is a function of the second derivative of the option price. The nonlinear equation is solved by a special class of numerical technique, called, the meshfree approximation using radial basis function. The numerical results are presented in diagrams and tables.

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