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In this research paper, we introduce a numerical approach to solve a particular type of nonlinear integro-differential equations derived from Volterra's population model. This model characterizes the growth of a biological species in a closed system and includes an integral term to consider the influence of toxin accumulation on the species, along with the conventional terms found in the logistic equation. The proposed technique estimates the solution of integro-differential equations utilizing the discrete Galerkin scheme using the moving least squares (MLS) algorithm. The locally weighted least squares polynomial fitting, known as the MLS method, is a valuable approach for approximating unknown functions. Since the offered scheme does not require any cell structures, it can be known as a meshless local discrete Galerkin method. Moreover, we obtain the error estimate of the proposed approach. The validity and efficiency of the newly developed technique are assessed over several nonlinear integro-differential equations. [ABSTRACT FROM AUTHOR]

An LT-BEM is used to find numerical solutions to an unsteady variable coefficients diffusion-convection equation governing problems of another class of anisotropic functionally graded media. A boundary-only integral equation is derived, following a transformation of the variable coefficients equation to a constant coefficients equation. The boundary-only integral equation is used to find the numerical solutions. Some problems considered are those for several new types of functionally graded materials of compressible or incompressible flow. The effects of the anisotropy and inhomogeneity of the considered materials on the solutions are also shown as to say that it is very important to take the anisotropy and inhomogeneity into account in experimental or practical studies for any applications. [ABSTRACT FROM AUTHOR]

The current investigation describes a computational technique to solve one- and two-dimensional Fredholm integral equations of the second kind. The method estimates the solution using the discrete collocation method by combining locally supported radial basis functions (RBFs) constructed on a small set of nodes instead of all points over the analysed domain. In this work, we employ the Gauss–Legendre integration rule on the influence domains of shape functions to approximate the local integrals appearing in the method. In comparison with the globally supported RBFs for solving integral equations, the proposed method is stable and uses much less computer memory. The scheme does not require any cell structures, so it is meshless. We also obtain the error analysis of the proposed method and demonstrate that the convergence rate of the approach is high. Illustrative examples clearly show the reliability and efficiency of the new method. [ABSTRACT FROM AUTHOR]

This article describes a technique for numerically solving a class of nonlinear boundary integral equations of the second kind with logarithmic singular kernels. These types of integral equations occur as a reformulation of boundary value problems of Laplace's equations with nonlinear Robin boundary conditions. The method uses thin plate splines (TPSs) constructed on scattered points as a basis in the discrete collocation method. The TPSs can be seen as a type of the free shape parameter radial basis functions which establish effective and stable methods to estimate an unknown function. The proposed scheme utilizes a special accurate quadrature formula based on the non-uniform Gauss-Legendre integration rule for approximating logarithm-like singular integrals appeared in the approach. The numerical method developed in the current paper does not require any mesh generations, so it is meshless and independent of the geometry of the domain. The algorithm of the presented scheme is accurate and easy to implement on computers. The error analysis of the method is provided. The convergence validity of the new technique is examined over several boundary integral equations and obtained results confirm the theoretical error estimates. [ABSTRACT FROM AUTHOR]

This paper proposes a numerical approach to approximate the unknown solution of some high-order fractional partial differential equations. The main idea of this approach is to transform the original problem into an equivalent integral equation that depends only on the boundary values. The linear radial basis functions are used as the main tool for approximating the non-homogeneous terms and time derivative. Also the Caputo's sense is applied to approximate time derivatives. Numerical results demonstrate the order of time steps is and when and , respectively. Finally to overcome the nonlinear terms, predictor-corrector scheme is employed. The efficiency and usefulness of proposed method are demonstrated by some numerical examples. [ABSTRACT FROM AUTHOR]

Existing literature on multicast routing protocols in wireless mesh networks (WMNs) from the view point of the links involved in routing are divided into two categories: schemes are aimed at multicast construction with minimal interference which is known as NP hard problem. In contrast, other methods develop network-coding-based solutions with the main objective of throughput maximization, which can effectively reduce the complexity of finding the optimal routing solution from exponential to polynomial time. The proposed framework in this paper is placed in the second category. In multi-channel multi-radio WMNs (MCMR WMNs), each node is equipped with multiple radios, each tuned on a different channel. In this paper, for the first time, we propose a cross-layer convex optimization framework for joint channel assignment and multicast throughput maximization in MCMR WMNs. The proposed method is composed of two phases: in the first phase, using cellular learning automata, channels are assigned to the links established between the radios of the nodes in a distributed fashion such that the minimal interference coefficient for each link is provided. Then, the resultant channel assignment scheme is utilized in the second phase for throughput maximization within an iterative optimization framework based on Lagrange relaxation and primal problem decomposition. We have conducted many experiments to contrast the performance of our solution against many representative approaches. [ABSTRACT FROM AUTHOR]

A numerical technique for solving a second-order nonlinear Neumann problem is presented. The authors' approach is based on semi-orthogonal B-spline wavelets. Two test problems are presented and numerical results are tabulated to show the efficiency of the proposed technique for the studied problem. [ABSTRACT FROM AUTHOR]

A time-stepping dual-reciprocity boundary element method is proposed for solving approximately an inverse problem of determining an unknown control parameter p(t) which is the coefficient of the solution u(x,y,t) in a diffusion equation in a two-dimensional region R . The diffusion equation is to be solved subject to suitably prescribed initial-boundary conditions. The presence of the unknown coefficient p(t) requires an extra condition. This takes the form of a non-local condition expressed in terms of an integral over R . The method is applied to solve a specific test problem. [ABSTRACT FROM AUTHOR]