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A number of works have been published in the scientific literature proposing the solution of heat diffusion problems by first transforming the relevant partial differential equation to the frequency domain. The purpose of this paper is to present a mesh-free strategy to assess transient heat propagation in the frequency domain, also allowing incorporating initial non-zero conditions.

The strategy followed here is based in Kansa's method, using the MQ RBF as a basis function. The resulting method is truly mesh-free, and does not require any domain or boundary integrals to be evaluated. The definition of good values for the free parameter of the MQ RBF is also addressed.

The strategy was found to be accurate in the calculation of both frequency and time-domain responses. The time evolution of the temperature considering an initial non-uniform distribution of temperatures compared well with a standard time-marching algorithm, based on an implicit Crank-Nicholson implementation. It was possible to calculate frequency-dependent values for the free parameter of the radial basis function.

As far as the authors are aware, previous implementations of the frequency domain heat transfer approach required domain integrals to be evaluated in order to implement non-zero initial conditions. This is totally avoided with the present formulation. Additionally, the method is truly mesh-free, accurate and does not require any element or background mesh to be defined.

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.

The purpose of this paper is to show that the meshless method based on radial basis functions (RBFs) collocation method is powerful, suitable and simple for solving one and two dimensional time fractional telegraph equation.

In this method the authors first approximate the time fractional derivatives of mentioned equation by two schemes of orders O(τ3−α) and O(τ2−α), 1/2<α<1, then the authors will use the Kansa approach to approximate the spatial derivatives.

The results of numerical experiments are compared with analytical solution, revealing that the obtained numerical solutions have acceptance accuracy.

The results show that the meshless method based on the RBFs and collocation approach is also suitable for the treatment of the time fractional telegraph equation.

The purpose of this study is to use the method of lines to solve the two-dimensional nonlinear advection–diffusion–reaction equation with variable coefficients.

The strictly positive definite radial basis functions collocation method together with the decomposition of the interpolation matrix is used to turn the problem into a system of nonlinear first-order differential equations. Then a numerical solution of this system is computed by changing in the classical fourth-order Runge–Kutta method as well.

Several test problems are provided to confirm the validity and efficiently of the proposed method.

For the first time, some famous examples are solved by using the proposed high-order technique.

The purpose of this paper is to obtain accurate numerical solutions of two-dimensional (2-D) and 3-dimensional (3-D) Klein–Gordon–Schrödinger (KGS) equations.

The use of linear barycentric interpolation differentiation matrices facilitates the computation of numerical solutions both in 2-D and 3-D space within reasonable central processing unit times.

Numerical simulations corroborate the efficiency and accuracy of the proposed method.

Linear barycentric interpolation method is applied to 2-D and 3-D KGS equations for the first time, and good results are obtained.

This study aims to propose a new numerical method for solving non-linear partial differential equations on irregular domains.

The main aim of the current paper is to propose a local meshless collocation method to solve the two-dimensional Klein-Kramers equation with a fractional derivative in the Riemann-Liouville sense, in the time term. This equation describes the sub-diffusion in the presence of an external force field in phase space.

First, the authors use two finite difference schemes to discrete temporal variables and then the radial basis function-differential quadrature method has been used to estimate the spatial direction. To discrete the time-variable, the authors use two different strategies with convergence orders O(τ1+γ) and O(τ2−γ) for 0 < γ < 1. Finally, some numerical examples have been presented to show the high accuracy and acceptable results of the proposed technique.

The proposed numerical technique is flexible for different computational domains.

The purpose of this paper is to extend the natural neighbour radial point interpolation method (NNRPIM) to the dynamic analysis (free vibrations and forced vibrations) of two‐dimensional, three‐dimensional and bending plate problems.

The NNRPIM shape‐function construction is briefly presented, as are the dynamic equations and the mode superposition method is used in the forced vibration analysis. Several benchmark examples of two‐dimensional and plate bending problems are solved and compared with the three‐dimensional NNRPIM formulation. The obtained results are compared with the available exact solutions and the finite element method (FEM) solutions.

The developed NNRPIM approach is a good alternative to the FEM for the solution of dynamic problems, once the obtained results with the EFGM shows a high similarity with the obtained FEM results and for the majority of the studied examples the NNRPIM results are more close to the exact solution results.

Comparing the FEM and the NNRPIM, the computational cost of the NNRPIM is higher.

The paper demonstrates extension of the NNRPIM to the dynamic analysis of two‐dimensional, three‐dimensional and bending plate problems. The elimination of the shear‐locking phenomenon in the NNRPIM plate bending formulation. The various solved examples prove a high convergence rate and accuracy of the NNRPIM.

Sharing information about work processes has proven to be difficult. This applies especially to information shared from those who participate in a process to those who remain outsiders. The purpose of this article is to increase understanding of how professionals document their work practices with a focus on information making by analysing how archaeologists document their information work in archaeological reports.

In total 47 Swedish archaeological reports published in 2018 were analysed using close reading and constant comparative categorisation.

Even if explicit narratives of methods and work process have particular significance as documentation of information making, the evidence of information making is spread out all over the report document in (1) procedural narratives, (2) descriptions of methods and tools, (3) actors and actants, (4) photographs, (5) information sources, (6) diagrams and drawings and (7) outcomes. The usability of reports as conveyors of information on information making depends more on how a forthcoming reader can live with it as a whole rather than how to learn of the details it recites.

The study is based on a limited number of documents representing one country and one scholarly and professional field.

Increased focus on the internal coherence of documentation and the complementarity of different types of descriptions could improve information sharing. Further, descriptions of concepts that refer to work activities and the situation when information came into being could similarly improve their usability.

There is little earlier research on how professionals and academics document and describe their information activities.

A comprehensive understanding of the determining factors and implications of the frameworks for appreciating the relationships between climate risks and cultural heritage remains deficient. To address the gap, the review analysed literature on the management of climate risk in cultural heritage. The review examines the strengths and weaknesses of climate risk management (CRM) frameworks and attendant implications for the conservation of cultural heritage.

The study adopted a two-phased systematic review procedure. In the first phase, the authors reviewed related publications published between 2017 and 2021 in Scopus and Google Scholar. Key reports published by organisations such as the United Nations Educational, Scientific and Cultural Organisation (UNESCO) and International Council on Monuments and Sites (ICOMOS) were identified and included in Phase Two to further understand approaches to CRM in cultural heritage.

Results established the changes in trend and interactions between factors influencing the adoption of CRM frameworks, including methods and tools for CRM. There is also increasing interest in adopting quantitative and qualitative methods using highly technical equipment and software to assess climate risks to cultural heritage assets. However, climate risk information is largely collected at the national and regional levels rather than at the cultural heritage asset.

The review establishes increasing implementation of CRM frameworks across national boundaries at place level using high-level technical skills and knowledge, which are rare amongst local organisations and professionals involved in cultural heritage management.

The review established the need for multi-sectoral, bottom-up and place-based approaches to improve the identification of climate risks and decision-making processes for climate change adaptation.

Taking the researchers’ perspective, the purpose of this paper is to examine the types of context information needed to preserve data’s meaning in ways that support data reuse.

This paper is based on a qualitative study of 105 researchers from three disciplinary communities: quantitative social science, archaeology and zoology. The study focused on researchers’ most recent data reuse experience, particularly what they needed when deciding whether to reuse data.

Findings show that researchers mentioned 12 types of context information across three broad categories: data production information (data collection, specimen and artifact, data producer, data analysis, missing data, and research objectives); repository information (provenance, reputation and history, curation and digitization); and data reuse information (prior reuse, advice on reuse and terms of use).

This paper extends digital curation conversations to include the preservation of context as well as content to facilitate data reuse. When compared to prior research, findings show that there is some generalizability with respect to the types of context needed across different disciplines and data sharing and reuse environments. It also introduces several new context types. Relying on the perspective of researchers offers a more nuanced view that shows the importance of the different context types for each discipline and the ways disciplinary members thought about them. Both data producers and curators can benefit from knowing what to capture and manage during data collection and deposit into a repository.