We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation.Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of or...We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation.Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations.For the temporal direction,we utilize the favorable boundary value methods owing to their advantageous stability properties.In addition,the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner.Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.展开更多
A higher-order compact scheme on the nine point 2-D stencil is developed for the steady stream-function vorticity form of the incompressible Navier-Stokes(NS)equations in spherical polar coordinates,which was used ear...A higher-order compact scheme on the nine point 2-D stencil is developed for the steady stream-function vorticity form of the incompressible Navier-Stokes(NS)equations in spherical polar coordinates,which was used earlier only for the cartesian and cylindrical geometries.The steady,incompressible,viscous and axially symmetric flow past a sphere is used as a model problem.The non-linearity in the N-S equations is handled in a comprehensive manner avoiding complications in calculations.The scheme is combined with the multigrid method to enhance the convergence rate.The solutions are obtained over a non-uniform grid generated using the transformation r=ex while maintaining a uniform grid in the computational plane.The superiority of the higher order compact scheme is clearly illustrated in comparison with upwind scheme and defect correction technique at high Reynolds numbers by taking a large domain.This is a pioneering effort,because for the first time,the fourth order accurate solutions for the problem of viscous flow past a sphere are presented here.The drag coefficient and surface pressures are calculated and compared with available experimental and theoretical results.It is observed that these values simulated over coarser grids using the present scheme aremore accuratewhen compared to other conventional schemes.It has also been observed that the flow separation initially occurred at Re=21.展开更多
In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by underst...In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by understandin<span>g geometry settings and mesh information. The concentration profile chan</span>ges over time, as does the intensity of the contour patterns. The OpenFoam solver gives you the confidence to compare the pattern result with efficient numerical algorithms on the Gray Scott model.展开更多
基金supported by the research grant UL020/08-Y2/MAT/JXQ01/FST,RG063/08-09S/SHW/FST from University of Macao,and the research grant from FDCT of Macao.
文摘We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential equation.Discretizing the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential equations.For the temporal direction,we utilize the favorable boundary value methods owing to their advantageous stability properties.In addition,the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type preconditioner.Numerical results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.
文摘A higher-order compact scheme on the nine point 2-D stencil is developed for the steady stream-function vorticity form of the incompressible Navier-Stokes(NS)equations in spherical polar coordinates,which was used earlier only for the cartesian and cylindrical geometries.The steady,incompressible,viscous and axially symmetric flow past a sphere is used as a model problem.The non-linearity in the N-S equations is handled in a comprehensive manner avoiding complications in calculations.The scheme is combined with the multigrid method to enhance the convergence rate.The solutions are obtained over a non-uniform grid generated using the transformation r=ex while maintaining a uniform grid in the computational plane.The superiority of the higher order compact scheme is clearly illustrated in comparison with upwind scheme and defect correction technique at high Reynolds numbers by taking a large domain.This is a pioneering effort,because for the first time,the fourth order accurate solutions for the problem of viscous flow past a sphere are presented here.The drag coefficient and surface pressures are calculated and compared with available experimental and theoretical results.It is observed that these values simulated over coarser grids using the present scheme aremore accuratewhen compared to other conventional schemes.It has also been observed that the flow separation initially occurred at Re=21.
文摘In this paper, a two-dimensional nonlinear coupled Gray Scott system is simulated with a finite difference scheme and a finite volume technique. Pre and post-processing lead to a new solution called GSmFoam by understandin<span>g geometry settings and mesh information. The concentration profile chan</span>ges over time, as does the intensity of the contour patterns. The OpenFoam solver gives you the confidence to compare the pattern result with efficient numerical algorithms on the Gray Scott model.
