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In this paper, various regularization methods are numerically implemented using the boundary element method (BEM) in order to solve the Cauchy steady‐state heat conduction problem in an anisotropic medium. The convergence and the stability of the numerical methods are investigated and compared. The numerical results obtained confirm that stable numerical results can be obtained by various regularization methods, but if high accuracy is required for the temperature, or if the heat flux is also required, then care must be taken when choosing the regularization method since the numerical results are substantially improved by choosing the appropriate method.

The purpose of this paper is to introduce a novel approach based on the high-order matrix derivative of the Bernstein basis and collocation method and its employment to solve an interesting and ill-posed model in the heat conduction problems, homogeneous backward heat conduction problem (BHCP).

By using the properties of the Bernstein polynomials the problems are reduced to an ill-conditioned linear system of equations. To overcome the unstability of the standard methods for solving the system of equations an efficient technique based on the Tikhonov regularization technique with GCV function method is used for solving the ill-condition system.

The presented numerical results through table and figures demonstrate the validity and applicability and accuracy of the technique.

A novel method based on the high-order matrix derivative of the Bernstein basis and collocation method is developed and well-used to obtain the numerical solutions of an interesting and ill-posed model in heat conduction problems, homogeneous BHCP with high accuracy.

To develop a numerical technique for solving the inverse source problem associated with the constant coefficients convection‐diffusion equation.

The proposed numerical technique is based on the boundary element method (BEM) combined with an iterative sequential quadratic programming (SQP) procedure. The governing convection‐diffusion equation is transformed into a Helmholtz equation and the ill‐conditioned system of equations that arises after the application of the BEM is solved using an iterative technique.

The iterative BEM presented in this paper is well‐suited for solving inverse source problems for convection‐diffusion equations with constant coefficients. Accurate and stable numerical solutions were obtained for cases when the number of sources is correctly estimated, overestimated, or underestimated, and with both exact and noisy input data.

The proposed numerical method is limited to cases when the Péclet number is smaller than 100. Future approaches should include the application of the BEM directly to the convection‐diffusion equation.

Applications of the results presented in this paper can be of value in practical applications in both heat and fluid flow as they show that locations and strengths for an unknown number of point sources can be accurately found by using boundary measurements only.

The BEM has not as yet been employed for solving inverse source problems related with the convection‐diffusion equation. This study is intended to approach this problem by combining the BEM formulation with an iterative technique based on the SQP method. In this way, the many advantages of the BEM can be applied to inverse source convection‐diffusion problems.

This work aims to estimate the unknown surface temperature distribution on the boundary of a heat conducting solid body from temperature measurements taken from another boundary where convective boundary condition is also known. A steady inverse heat conduction problem is described for an arbitrary three‐dimensional body. A gradient‐based inverse method combined with B‐spline function specification is employed to solve the inverse problem. The validity of the proposed method is verified with computational results.

Non‐linear reaction‐diffusion processes with cross‐diffusion in two‐dimensional, anisotropic media are analyzed by means of an implicit, iterative, time‐linearized approximate factorization technique as functions of the anisotropy of the heat and species diffusivity tensors, the Soret and Dufour cross‐diffusion effects, and five types of boundary conditions. It is shown that anisotropy and cross‐diffusion deform the reaction front and affect the front velocity, and the magnitude of these effects increases as the magnitude of the off‐diagonal components of the heat and species diffusivity tensors is increased. It is also shown that the five types of boundary conditions employed in this study produce similar results except when there is either strong anisotropy in the species or heat diffusivity tensors and there are no Soret and Dufour effects, or the species and heat diffusivity tensors are isotropic, but the anisotropy of the Soret and Dufour effects is important. If the species and heat diffusivity tensors are isotropic, the effects of either the Soret or the Dufour cross‐diffusion effects are small for the cases considered in this study. The time required to achieve steady state depends on the anisotropy of the heat and diffusivity tensors, the cross‐diffusion effects, and the boundary conditions.

The aim of this paper is to find the optimal values of the reaction rates coefficients for the combustion of a methane/air mixture for a given reduced reaction mechanism which has a high appropriateness with full reaction mechanism.

A multi‐objective genetic algorithm (GA) was used to determine new reaction rate parameters (A's, β's, and E_a's in the non‐Arrhenius expressions). The employed multi‐objective structure of the GA allows for the incorporation of perfectly stirred reactor (PSR), laminar premixed flames, opposed flow diffusion flames, and homogeneous charge compression ignition (HCCI) engine data in the inversion process, thus enabling a greater confidence in the predictive capabilities of the reaction mechanisms obtained.

The results of this study demonstrate that the GA inversion process promises the ability to assess combustion behaviour for methane, where the reaction rate coefficients are not known. Moreover it is shown that GA can consider a confident method to be applied, straightforwardly, to the combustion chambers, in which complex reactions are occurred.

In this paper, GA is used in more complicated combustion models with fewer assumptions. Another consequence of this study is less CPU time in converging to final solutions.

The purpose of this paper is to study how variables such as the region’s overall image, the perceived quality of its financial entities, and consumer ethnocentrism affect the intention to choose regional banks. Special attention is paid to the moderating role played by familiarity.

A structural equation model was used with a survey of 427 bank customers.

The results show direct and indirect effects of regional image, perceived quality of regional banks and consumer ethnocentrism on the intention to choose regional banks. The moderating effect of familiarity is not confirmed.

The financial crisis experienced in southern European countries has forced them to carry out a restructuring of the banking sector based on mergers that provide greater solvency and stability. In Spain, this has meant small regional banks merging with each other to form larger national banks. This involves a loss of their regional identity and a change in their positioning to date. It is interesting to understand the value to customers of the regional attribute when choosing a bank and the possible consequences of merging with other banks.

Globalisation has made origin an attractive attribute that can be used to differentiate products. However, there are still gaps in this field, especially in relation to region-of-origin (ROO) and the influence of certain moderating variables on this effect. This paper sheds some light on the study of the ROO effect in the financial sector, a field that is still relatively unexplored in this context.