This paper concerns numerical computation of a non-standard fourth order eigenvalue problem. For high order problems, Discontinuous Galerkin methods are competitive since they avoid some difficulties arising from other approaches. We show the well-posedness of the source problem. An interior penalty discontinuous Galerkin method using Lagrange elements (C0IPG) is proposed and its convergence is...

The present paper includes the local and semilocal convergence analysis of a fourth-order method based on quadrature formula in Banach spaces. weaker hypotheses used are only first Fréchet derivative. new approach provides residual errors, number iterations, radii, expected order convergence, estimates uniqueness solution. Such not provided approaches using Taylor expansions involving higher-or...

We derive a new compact high-order finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. To prove results on the unconditional stability in the sense of von Neumann we perform a thorough Fourier analysis of the problem and deduce convergence of our scheme. We present results of numerical exper...

Abstract Many multipoint iterative methods without memory for solving non-linear equations in one variable are found the literature. In particular, there that provide fourth-order, eighth-order or sixteenth-order convergence using only, respectively, three, four five function evaluations per iteration step, thus supporting Kung-Traub conjecture on optimal order of convergence. This paper shows ...