Accurate radial basis functions technique for competitive and efficient solutions of non-linear Black-Scholes equations

ABSTRACTObjective: This article aims to solve the non-linear Black Scholes (BS) equation for European call options using Radial Basis Function (RBF) Multi-Quadratic (MQ) Method.Methodology / Approach: This work uses the MQ RBF method applied to the solution of two complex models of nonlinear BS equation for prices of European call options with modified volatility. Linear BS models are also solved to visualize the effects of modified volatility. Additionally, an adaptive scheme is implemented in time based on the Runge-Kutta-Fehlberg (RKF) method.

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The Conical Radial Basis Function for Partial Differential Equations

Journal of Mathematics ◽

10.1155/2020/6664071 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

J. Zhang ◽

F. Z. Wang ◽

E. R. Hou

Keyword(s):

Radial Basis Function ◽

Boundary Value Problems ◽

Basis Function ◽

Boundary Value ◽

Computational Cost ◽

Basis Functions ◽

Simple Scheme ◽

Collocation Points ◽

Radial Basis ◽

Radial Basis Function Method

The performance of the parameter-free conical radial basis functions accompanied with the Chebyshev node generation is investigated for the solution of boundary value problems. In contrast to the traditional conical radial basis function method, where the collocation points are placed uniformly or quasi-uniformly in the physical domain of the boundary value problems in question, we consider three different Chebyshev-type schemes to generate the collocation points. This simple scheme improves accuracy of the method with no additional computational cost. Several numerical experiments are given to show the validity of the newly proposed method.

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Radial basis function network for non-linear EDC in optical communication OOK system

2006 Optical Fiber Communication Conference and the National Fiber Optic Engineers Conference ◽

10.1109/ofc.2006.215528 ◽

2006 ◽

Cited By ~ 2

Author(s):

G. Katz ◽

D. Sadot

Keyword(s):

Radial Basis Function ◽

Optical Communication ◽

Basis Function ◽

Radial Basis Function Network ◽

Non Linear ◽

Radial Basis ◽

Function Network

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Differential Evolution-Based Optimization of Kernel Parameters in Radial Basis Function Networks for Classification

International Journal of Applied Evolutionary Computation ◽

10.4018/jaec.2013010104 ◽

2013 ◽

Vol 4 (1) ◽

pp. 56-80 ◽

Cited By ~ 5

Author(s):

Ch. Sanjeev Kumar Dash ◽

Ajit Kumar Behera ◽

Satchidananda Dehuri ◽

Sung-Bae Cho

Keyword(s):

Neural Networks ◽

Differential Evolution ◽

Radial Basis Function ◽

Basis Function ◽

Learning Algorithm ◽

Basis Functions ◽

Second Phase ◽

Rbf Neural Networks ◽

Radial Basis ◽

Two Phases

In this paper a two phases learning algorithm with a modified kernel for radial basis function neural networks is proposed for classification. In phase one a new meta-heuristic approach differential evolution is used to reveal the parameters of the modified kernel. The second phase focuses on optimization of weights for learning the networks. Further, a predefined set of basis functions is taken for empirical analysis of which basis function is better for which kind of domain. The simulation result shows that the proposed learning mechanism is evidently producing better classification accuracy vis-à-vis radial basis function neural networks (RBFNs) and genetic algorithm-radial basis function (GA-RBF) neural networks.

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Multilevel RBF collocation method for the fourth-order thin plate problem

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691320500794 ◽

2020 ◽

pp. 2050079

Author(s):

Lanling Ding ◽

Zhiyong Liu ◽

Qiuyan Xu

Keyword(s):

Radial Basis Function ◽

Collocation Method ◽

Radial Basis Functions ◽

Thin Plate ◽

Fourth Order ◽

Basis Function ◽

Research Method ◽

Meshfree Method ◽

Basis Functions ◽

Radial Basis

The radial basis functions meshfree method is a research method for thin plate problem which has gradually developed into a more mature meshfree method. It includes finite element, radial basis functions meshfree collocation method, etc. In this paper, we introduce the multilevel radial basis function collocation method for the fourth-order thin plate problem. We use nonsymmetric Kansa multilevel radial basis function collocation method to solve the fourth-order thin plate problem. Two numerical examples based on Wendland’s [Formula: see text] and [Formula: see text] functions are given to examine that the convergence of the multilevel radial basis function collocation method which is good for solving the fourth-order thin plate problem.

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