In this paper, for analyses of metal forming problems, a point collocation method (PCM) with a boundary layer of finite element is developed. PCMs have some advantages such as no mesh, no integration. While, the robustness of the PCMs is an issue especially when scattered and random points are used. To improve the robustness, some studies suggest that the positivity conditions can be important ...

The aim of this paper is to design a new family of numerical methods of arbitrarily high order for systems of rst-order diierential equations which are to be termed pseudo two-step Runge-Kutta methods. By using collocation techniques, we can obtain an arbitrarily high-order stable pseudo two-step Runge-Kutta method with any desired number of implicit stages in retaining the two-step nature. In ...

For solving electroencephalographic forward problem, coupled method of finite element method FEM and fast moving least square reproducing kernel method FMLSRKM which is a kind of meshfree method is proposed. Current source modeling for FEM is complicated, so source region is analyzed usingmeshfreemethod. First order of shape function is used for FEM and second order for FMLSRKM because FMLSRKM ...

Currently there are two general ways to solve stiff differential equations numerically. The first approach is based on implicit methods and the second uses explicit stabilized Runge–Kutta methods, also known as Chebyshev methods. Implicit methods are great for very stiff problems of not very large dimension, while stabilized explicit methods are efficient for very big systems of not very large ...

Almost nothing decisive has been said about collocation methods for solving SPDEs. Among the best of such SPDEs the Burgers equation shows a prototypical model for describing the interaction between the reaction mechanism, convection effect, and diffusion transport. This paper discusses spectral collocation method to reduce stochastic Burgers equation to a system of stochastic ordinary differen...

In this work we present numerical methods for the solution of Fredholm integral equations of the second type for smooth and piecewise smooth surfaces We use a collocation method based on piecewise polynomial interpolation of the solution We consider only collocation methods for which the collocation nodes are interior to each triangular face In Chapter II we give the general framework for collo...

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of “blow-up collocation solution” and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we d...

In this paper we study the numerical solution of nonlinear Volterra integrodifferential equations with infinite delay by spline collocation and related Runge-Kutta type methods. The kernel function in these equations is of the form k(t,s,y(t),y(s)), with a representative example given by Volterra's population equation, where we have k(t, s, y(t),y(s)) = a(t s) ■ G(y(t), y(s)). '

In this study, a spectral collocation domain decomposition method is developed for the numerical solution of second and fourth order problems in circular domains. The method is applied to the Navier-Stokes equations and its performance is investigated in the cases of the stream function and the stream function-vorticity formulations.

A lumped heat transfer model and parameter estimation technique are proposed for determining key parameters associated with a heat flux Differential Scanning Calorimeter (DSC). The development of a mathematical algorithm utilizing this model and technique is illustrated in Part I of this two-part paper. In Part II, a computational algorithm which has been constructed for the proposed method is ...