LaxWendroffBurgers1D.zip - Simple implementation of the Taylor-Galerkin discretization for the 1D Burgers equation, which reduces to the Lax-Wendroff scheme when the element size is constant. Description of derivation included. For a practical usage, run a coarse mesh/time-step size combination and, based on the max(abs(u)), re-estimate dt using a finer mesh and CFL = 0.8. Although a higher value is technically more accurate, in practise the spurious oscillations (typical of LW scheme for hyperbolic conservation) impose and additional, hard-to-predict penalty on stability. Implementation of a "real" viscous term helps controlling the oscillations, but imposes another restriction on mesh/time-step size ratio (B = u_max*((dt^2)/(dx^2)) ). Remark that, even with oscillating solution near discontinuities, it is still better at capturing shocks than 1st order upwinding methods.,2019-11-17 22:25:09,下载2次
Burgers_equation.zip - The 1D Burgers equation is solved using explicit spatial discretization (upwind and central difference) with periodic boundary conditions on the domain (0,2). The 2D case is solved on a square domain of 2X2 and both explicit and implicit methods are used for the diffusive terms. Dirichlet boundary conditions are used along the edges of the domain.,2019-11-17 22:22:50,下载2次
Runge-Kutta-Nystrom integrator.zip - RKN1210 12th/10th order Runge-Kutta-Nystr?m integrator
RKN1210() is a 12th/10th order variable-step numerical integrator for second-order ordinary differential equations of the form
y'' = f(t, y) (1)
with initial conditions
y(t0) = y0
y'(t0) = yp0 (2)
This second-order differential equation is integrated with a Runge-Kutta-Nystr?m method using 17 function evaluations per step. RKN12(10) is a very high-order method, to be used in problems with *extremely* stringent error tolerances.,2019-11-17 21:27:22,下载0次
fd1d_heat_explicit.rar - FD1D_HEAT_EXPLICIT is a FORTRAN90 program which solves the time-dependent 1D heat equation, using the finite difference method in space, and an explicit version of the method of lines to handle integration in time.
,2010-12-22 14:08:23,下载11次
fd1d_bvp_prb.rar - FD1D_BVP is a FORTRAN90 program which applies the finite difference method to solve a two point boundary value problem in one spatial dimension.
The boundary value problem (BVP) that is to be solved has the form:
,2010-12-22 14:07:22,下载5次
fd1d_burgers_lax.rar - FD1D_BURGERS_LAX is a FORTRAN90 program which solves the nonviscous time-dependent Burgers equation using finite differences and the Lax-Wendroff method.
The function u(x,t) is to be solved for in the equation
,2010-12-22 14:06:26,下载26次
fd1d_burgers_leap.rar - FD1D_BURGERS_LEAP is a FORTRAN90 program which solves the nonviscous time-dependent Burgers equation using finite differences and the leapfrog method.
The function u(x,t) is to be solved for in the equation:
,2010-12-22 14:05:11,下载7次
channel.rar - channel 问题 求解粘性不可压NS方程 ,2010-12-22 14:03:04,下载19次
functionzRR.rar - ％code2_1 for lecture 1 Simpson s rule ,2006-03-15 21:34:34,下载132次
functionz1.rar - 寻找三次样条多项式需要求解大量的线性方程。实际上，给定N个断点，就要寻找N-1个三次多项式，每个多项式有4个未知系数。这样，所求解的方程组包含有4*(N-1)个未知数。把每个三次多项式列成特殊形式，并且运用各种约束，通过求解N个具有N个未知系数的方程组，就能确定三次多项式。
,2006-03-15 21:22:27,下载161次
functionz.rar -
在三次样条中，要寻找三次多项式，以逼近每对数据点间的曲线。在样条术语中，这些数据点称之为断点。因为，两点只能决定一条直线，而在两点间的曲线可用无限多的三次多项式近似。因此，为使结果具有唯一性。在三次样条中，增加了三次多项式的约束条件。通过限定每个三次多项式的一阶和二阶导数，使其在断点处相等，就可以较好地确定所有内部三次多项式。此外，近似多项式通过这些断点的斜率和曲率是连续的。然而，第一个和最后一个三次多项式在第一个和最后一个断点以外，没有伴随多项式。因此必须通过其它方法确定其余的约束。最常用的方法，也是函数spline所采用的方法，就是采用非扭结(not-a-knot)条件。这个条件强迫第一个和第二个三次多项式的三阶导数相等。对最后一个和倒数第二个三次多项式也做同样地处理。
,2006-03-15 21:19:29,下载316次