Discrete linear multistep block method of uniform order for the solution of first order initial value problems (IVPs) in ordinary differential equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. ...

Two collocation-based methods utilizing the novel Bessel polynomials (with positive coefficients) are developed for solving non-linear Troesch’s problem. In first approach, by expressing unknown solution and its second derivative in terms of matrix form along with some collocation points, governing equation transforms into a algebraic equation. technique quasi-linearization is employed to linea...

In this paper, we develop an efficient spectral method for numerically solving the nonlinear Volterra integral equation with weak singularity and delays. Based on symmetric collocation points, is illustrated, convergence results are obtained. end, two numerical experiments carried out to confirm theoretical results.

Quartic non-polynomial spline function approximation in off step points is developed, for the solution of fourth-order boundary value problems. Using consistency relation of such spline and suitable choice of parameter,we have obtained second, fourth and sixth orders methods. Convergence analysis of sixth order method has been given. The methods are illustrated by some examples, to verify the or...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In both the real variable and Complex Variable Boundary Element Methods (CVBEM), nodal points are typically ...

We propose a methodology for sampling from time-integrated stochastic bridges, i.e., random variables defined as ∫t1t2f(Y(t))dt conditional on Y(t1)=a and Y(t2)=b, with a,b∈R. The techniques developed in Grzelak et al. (2019) – the Stochastic Collocation Monte Carlo sampler Liu (2020) Seven-League scheme are applied this purpose. Notably, bridge distribution is approximated using polynomial cha...

Non–intrusive Simplex Elements Stochastic Collocation, Stochastic Collocation with Clenshaw–Curtis points, and the Padé–Legendre method are applied to the transonic RAE 2822 airfoil test case of the NODESIM Workshop on Quantification of CFD Uncertainties. Uncertainty in a combination of the free stream Mach number M∞, angle of attack α, and thickness–to–chord ratio t/c described by uniform and ...

An analysis method based on a multidomain pseudospectral method is proposed for calculating the band diagrams of two-dimensional photonic crystals and is shown to possess excellent numerical convergence behavior and accuracy. The proposed scheme utilizes the multidomain Chebyshev collocation method. By applying Chebyshev-Lagrange interpolating polynomials to the approximation of spatial derivat...

Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment. In this work, I present a general surface integral equation and BEM discretization that remove this limitation and allow BEM modeling of general piecewise-h...