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The study aims to present a new meshless method based on the Taylor series expansion. The compact supported radial basis functions (CSRBFs) are very attractive, can be considered as a numerical tool for the engineering problems and used to obtain the trial solution and its derivatives without differentiating the basis functions for a meshless method. A meshless based on the CSRBF and Taylor series method has been developed for the solutions of engineering problems.

This paper is devoted to present a truly meshless method which is called a radial basis Taylor series method (RBTSM) based on the CSRBFs and Taylor series expansion (TSE). The basis function and its derivatives are obtained without differentiating CSRBFs.

The RBTSM does not involve differentiation of the approximated function. This property allows us to use a wide range of CSRBF and weight functions including the constant one. By using a different number of terms in the TSE, the global convergence properties of the RBTSM can be improved. The global convergence properties are satisfied by the RBTSM. The computed results based on the RBTSM shows excellent agreement with results given in the open literature. The RBTSM can provide satisfactory results even with the problem domains which have curved boundaries and irregularly distributed nodes.

The CSRBFs have been widely used for the construction of the basic function in the meshless methods. However, the derivative of the basis function is obtained with the differentiation of the CSRBF. In the RBTSM, the derivatives of the basis function are obtained by using the TSE without differentiating the CSRBF.

The purpose of this paper is to develop two meshfree algorithms based on multiquadric radial basis functions (RBFs) and differential quadrature (DQ) technique for numerical simulation and to capture the shocks behavior of Burgers’ type problems.

The algorithms convert the problems into a system of ordinary differential equations which are solved by the Runge–Kutta method.

Two meshfree algorithms are developed and their stability is discussed. Numerical experiment is done to check the efficiency of the algorithms, and some shock behaviors of the problems are presented. The proposed algorithms are found to be accurate, simple and fast.

The present algorithms LRBF-DQM and GRBF-DQM are based on radial basis functions, which are new for Burgers’ type problems. It is concluded from the numerical experiments that LRBF-DQM is better than GRBF-DQM. The algorithms give better results than available literature.

The purpose of this paper is to provide an effective and simple technique to structural damage identification, particularly to identify a crack in a structure. Artificial neural networks approach is an alternative to identify the extent and location of the damage over the classical methods. Radial basis function (RBF) networks are good at function mapping and generalization ability among the various neural network approaches. RBF neural networks are chosen for the present study of crack identification.

Analyzing the vibration response of a structure is an effective way to monitor its health and even to detect the damage. A novel two‐stage improved radial basis function (IRBF) neural network methodology with conventional RBF in the first stage and a reduced search space moving technique in the second stage is proposed to identify the crack in a cantilever beam structure in the frequency domain. Latin hypercube sampling (LHS) technique is used in both stages to sample the frequency modal patterns to train the proposed network. Study is also conducted with and without addition of 5% white noise to the input patterns to simulate the experimental errors.

The results show a significant improvement in identifying the location and magnitude of a crack by the proposed IRBF method, in comparison with conventional RBF method and other classical methods. In case of crack location in a beam, the average identification error over 12 test cases was 0.69 per cent by IRBF network compared to 4.88 per cent by conventional RBF. Similar improvements are reported when compared to hybrid CPN BPN networks. It also requires much less computational effort as compared to other hybrid neural network approaches and classical methods.

The proposed novel IRBF crack identification technique is unique in originality and not reported elsewhere. It can identify the crack location and crack depth with very good accuracy, less computational effort and ease of implementation.

Global optimization in electrical engineering using stochastic methods requires usually a large amount of CPU time to locate the optimum, if the objective function is calculated either with the finite element method (FEM) or the boundary element method (BEM). One approach to reduce the number of FEM or BEM calls using neural networks and another one using multiquadric functions have been introduced recently. This paper compares the efficiency of both methods, which are applied to a couple of test problems and the results are discussed.

In the new era of highly developed Internet information, the prediction of the development trend of network public opinion has a very important reference significance for monitoring and control of public opinion by relevant government departments.

Aiming at the complex and nonlinear characteristics of the network public opinion, considering the accuracy and stability of the applicable model, a network public opinion prediction model based on the bald eagle algorithm optimized radial basis function neural network (BES-RBF) is proposed. Empirical research is conducted with Baidu indexes such as “COVID-19”, “Winter Olympic Games”, “The 100th Anniversary of the Founding of the Party” and “Aerospace” as samples of network public opinion.

The experimental results show that the model proposed in this paper can better describe the development trend of different network public opinion information, has good stability in predictive performance and can provide a good decision-making reference for government public opinion control departments.

A method for optimizing the central value, weight, width and other parameters of the radial basis function neural network with the bald eagle algorithm is given, and it is applied to network public opinion trend prediction. The example verifies that the prediction algorithm has higher accuracy and better stability.

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.

This paper aims to develop a meshfree algorithm based on local radial basis functions (RBFs) combined with the differential quadrature (DQ) method to provide numerical approximations of the solutions of time-dependent, nonlinear and spatially one-dimensional reaction-diffusion systems and to capture their evolving patterns. The combination of local RBFs and the DQ method is applied to discretize the system in space; implicit multistep methods are subsequently used to discretize in time.

In a method of lines setting, a meshless method for their discretization in space is proposed. This discretization is based on a DQ approach, and RBFs are used as test functions. A local approach is followed where only selected RBFs feature in the computation of a particular DQ weight.

The proposed method is applied on four reaction-diffusion models: Huxley’s equation, a linear reaction-diffusion system, the Gray–Scott model and the two-dimensional Brusselator model. The method captured the various patterns of the models similar to available in literature. The method shows second order of convergence in space variables and works reliably and efficiently for the problems.

The originality lies in the following facts: A meshless method is proposed for reaction-diffusion models based on local RBFs; the proposed scheme is able to capture patterns of the models for big time T; the scheme has second order of convergence in both time and space variables and Nuemann boundary conditions are easy to implement in this scheme.

This work compares the performance of the three boundary element techniques for solving Helmholtz problems: dual reciprocity, multiple reciprocity and direct interpolation. All techniques transform domain integrals into boundary integrals, despite using different principles to reach this purpose.

Comparisons here performed include the solution of eigenvalue and response by frequency scanning, analyzing many features that are not comprehensively discussed in the literature, as follows: the type of boundary conditions, suitable number of degrees of freedom, modal content, number of primitives in the multiple reciprocity method (MRM) and the requirement of internal interpolation points in techniques that use radial basis functions as dual reciprocity and direct interpolation.

Among the other aspects, this work can conclude that the solution of the eigenvalue and response problems confirmed the reasonable accuracy of the dual reciprocity boundary element method (DRBEM) only for the calculation of the first natural frequencies. Concerning the direct interpolation boundary element method (DIBEM), its interpolation characteristic allows more accessibility for solving more elaborate problems. Despite requiring a greater number of interpolating internal points, the DIBEM has presented higher-quality results for the eigenvalue and response problems. The MRM results were satisfactory in terms of accuracy just for the low range of frequencies; however, the neglected higher-order primitives impact the accuracy of the dynamic response as a whole.

There are safe alternatives for solving engineering stationary dynamic problems using the boundary element method (BEM), but there are no suitable comparisons between these different techniques. This paper presents the particularities and detailed comparisons approaching the accuracy of the three important BEM techniques, aiming at response and frequency evaluation, which are not found in the specialized literature.

The purpose of this research paper is to investigate and model the fused deposition modelling (FDM) process to predict the mechanical attributes of 3D printed specimens.

By exploiting the main effect plots, a Taguchi L18 orthogonal array is used to investigate the effects of such parameters on three mechanical attributes of the 3D printed specimens. A radial-based integrated network is then developed to map the eight FDM parameters to the three mechanical attributes for both PEEK and PEKK. Such an integrated network maps and predicts the mechanical attributes through two consecutive phases that consist of several radial basis functions (RBFs).

Validated on a set of further experiments, the integrated network was successful in predicting the mechanical attributes of the 3D printed specimens. It also outperformed the well-known RBF network with an overall improvement of 24% in the coefficient of determination. The integrated network is also further validated by predicting the mechanical attributes of a medical-surgical implant (i.e. the MidFace Rim) as an application.

The main aim of this paper is to accurately predict the mechanical properties of parts produced using the FDM process. Such an aim requires modelling a highly dimensional space to represent highly nonlinear relationships. Therefore, a radial-based integrated network based on the combination of composition and superposition of radial functions is developed to model FDM using a limited number of data points.

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The purpose of this paper is to address the solution of the Motz problem using the radial basis function (RBF) method, which is a truly meshfree scheme.

Both the global RBF collocation method (also known as Kansa's method) and the recently proposed local RBF‐based differential quadrature (LRBFDQ) method are considered. In both cases, it is shown that the accuracy of the solution can be significantly increased by using special functions which capture the behavior of the singularity. In the case of global collocation, the functional space spanned by the RBF is enlarged by adding singular functions which capture the behavior of the local singular solution. In the case of local collocation, the problem is modified appropriately in order to eliminate the singularities from the formulation.

The paper shows that the exponential convergence both with increasing resolution and increasing shape parameter, which is typical of the RBF method, is lost in problems containing singularities. The accuracy of the solution can be increased by collocation of the partial differential equation (PDE) at boundary nodes. However, in order to restore the exponential convergence of the RBF method, it is necessary to use special functions which capture the behavior of the solution near the discontinuity.

The paper uses Motz's problem as a prototype for problems described by elliptic partial differential equations with boundary singularities. However, the results obtained in the paper are applicable to a wide range of problems containing boundaries with conditions which change from Dirichlet to Neumann, thus leading to singularities in the first derivatives.

The paper shows that both the global RBF collocation method and the LRBFDQ method, are truly meshless methods which can be very useful for the solution of elliptic problems with boundary singularities. In particular, when complemented with special functions that capture the behavior of the solution near the discontinuity, the method exhibits exponential convergence both with resolution and with shape parameter.