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Showing 1 to 20 of 75 for “"finite-difference scheme"”.
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DGM-FD: A Finite Difference Scheme Based on the Discontinuous Galerkin Method
… adaptability to different mesh structures. Finite difference and finite element methods are commonly used numerical schemes in CAA. Finite difference methods have the advantages of ease of use as well as high order convergence, but often require a uniform grid, and stable boundary closure …
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A WENO finite difference scheme for a new class of Hamilton-Jacobi equations in electroelastostatics
… (1983) proved that a certain type of first-order finite difference method converges to the viscosity solution of a special class of Hamilton-Jacobi equations. From then on several successful methods of high-order approximation have been proposed in the literature, including the so-called WENO …
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Level-dependent volatility in jumping short-rate models
… will price such claims using an implicit finite difference scheme to implement a modelling framework that prices bonds, bond options and caplets with scheduled shocks to the short-term interest rate to simulate macroeconomic announcements and other sudden developments. This dissertation …
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Machine learning for pricing European basket options
… European basket option. Next, we introduce the finite difference scheme to price the European basket option for given parameters such as risk-free interest rates, maturities and so on. However, for approximating the European basket option for different risk-free interest rates, maturities and …
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Numerical Solutions to PDE Representations of Derivatives with Bilateral Counterparty Risk and Funding Costs
… (2011). In particular, we use Crank-Nicolson finite-difference scheme to solve Black-Scholes risk-free PDE, for European and American options, and show how this numerical solution approach is extendable to solve the risky PDE for the value of the same derivative using the same …
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Finite difference approach for predicting probabilistic life of a composite cylinder subjected to thermal random loads
… equation in cylindrical coordinates. An implicit finite difference scheme is developed to obtain temperature responses inside the cylinder. Given the linear elastic behavior of materials involved, induced stresses and strains are evaluated at the end of each time step of the finite difference …
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A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.
… observed in field experiments. The implicit finite difference scheme with the shifted Grunwald approximation discritizing the fractional advection-diffusion equation unconditionally stable. We add an additional non-linear, Lipschitz continuous term to account for reactions and we solve the …
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A Numerical Method for Computing Radially Symmetric Solutions of a Dissipative Nonlinear Modified Klein-Gordon Equation
In this paper we develop a finite-difference scheme to approximate radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation in an open sphere around the origin, with constant internal and external damping coefficients and nonlinear term of the form G' (w) = w ^p, with …
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Phase-field simulation of solidification with moving solids
… solids. This methodology is implemented using a finite difference scheme and a semi-implicit integration method. Pure translation and pure rotation cases are demonstrated and a preliminary simulation of applied shear on a particle is presented. These results demonstrate that the model shows …
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Unsteady flow in the Third Navigation Channel, Gezhouba Water Control Project, China
… St Venant Equations, the Preissmann's implicit finite difference scheme, and the double sweep algorithm, a mathematical model for one-dimensional subcritical unsteady flow in the Third Navigation Channel at the Gezhouba Water Control Project, China, has been developed. The model has been …
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NEW COMPUTATIONAL METHODS FOR OPTIMAL CONTROL OF PARTIAL DIFFERENTIAL EQUATIONS
… Chaper 3, we present a new second-order leapfrog finite difference scheme in time for solving the first-order necessary optimality system of the linear parabolic optimal control problems. The new leapfrog scheme is shown to be unconditionally stable and it provides a second-order accuracy, while …
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A Dynamical Study of the Evolution of Pressure Waves Propagating through a Semi-Infinite Region of Homogeneous Gas Combustion Subject to a Time-Harmonic Signal at the Boundary
… with the long-time solution obtained by the finite-difference scheme; again, ensuring that the transient effects have dissipated. Since the finite-difference scheme requires a right boundary, its location is chosen so that the wave dissipates in amplitude enough so that any reflections from …
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DEVELOPMENT AND APPLICATIONS OF MACHINE/DEEP LEARNING TECHNIQUES IN FLUID DYNAMICS
… differentiation-based PINNs are improved by the finite difference scheme, and the proposed FD-PINNs are validated using incompressible isothermal and thermal flows.
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Formulações de elementos finitos bi e tridimensionais para simulação em paralelo de escoamentos em reservatórios de petróleo
Finite element formulations oriented to distributed memory parallel machines are proposed and analized to simulate incompressible miscible flow in porous media with applicationto petroleum reservoir engineering. The mathematical model consists in a system of a partial differential equations given …
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Interactions and orientation in concentrated suspensions of rigid rods: Theory and experiment
… diffusion. This equation is solved using a finite difference scheme and the results are presented versus experiments with suspensions with planar orientation in planar stretching flow. Experiments and simulation agree that increasing concentrations result in increased interaction-based …
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Implementation of Bivariate Unspanned Stochastic Volatility Models
… priced using an Alternating Direction Implicit finite difference scheme. We then implement an Unscented Kalman filter — a non-linear extension of the Kalman filter, which is a popular method for inferring state variable values — to recover the latent state variables from market observable data
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Finite-Difference and Analytic-Gradient Approaches for Simulating Vibrational Circular Dichroism Using Second-Order Møller-Plesset Perturbation Theory and Configuration Interaction
… basis sets. Next, we introduce a finite-difference scheme for computing the atomic axial tensor (AAT), a required quantity for VCD simulation, for the second-order Møller-Plesset perturbation (MP2) theory and configuration interaction with double excitations (CID) electronic …
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Investigation of Thermocapillary Flows Around Hemispherical Bubbles
… and constant wall temperature. A second order finite difference scheme was adopted for the diffusion terms in the governing equations, while stable upwind schemes were used for the non-linear convective terms. The elliptic stream-function was determined by a relaxation technique. The numerical …
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Development of a numerical method to solve the three-dimensional compressible laminar boundary-layer equations with application to elliptical cones at angle of attack
… solution technique which employs an implicit finite-difference scheme that is stable for negative transverse velocities is developed. The solutions for some 10° vertical half-angle elliptical cones of varying ellipticity ratios at up to 8° angle of attack at a Mach number of 7.95 are …
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Development of a reverse flood routing technique using the implicit method
… and depth, were computed using an implicit, finite difference scheme. A discharge hydrograph and rating curve supplied the initial values of discharge and depth along the downstream column of grid points. Boundary values of discharge were known along the top row and bottom row of grid points …
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