For solving biparabolic equation, the author presents two new classes of three layered implicit difference schemes with tridigonal matrix of coefficients. Their local truncation errors are in the order of O(τ 2+h 2+τh) and O(τ 2+h 2+(τh) 2) respectively.
Two absolute stable and high accuracy semi-explicit difference schemes where r= qt/h3 for solving the initial boundary value problems of the dispersive equation ut = auxxx are constructed. Thc local truncation errors for these difference schemes arc O(t2+ h4+t2/h2)
A two layered scheme is obtained when parameters α =1/2, β =0. These schemes are proved to be absolutely stable for all positive integers m and for arbitrarily chosen non negative parameters α≥0, β ≥0; and their truncation errors are all in the order of O(( Δ t) 2+( Δ x) 6) .
A class of new three-layer difference sehemes containing biparameters are constructed for convective equation Ut=aUx A double-layer scheme will be obtained in case α= 1/2,β=0. These schemes are all absolutely stable for arbirarily nonnegative parameters, with local truncation error of O(Δt2+Δx4).
A three-level explicit difference scheme is proposed for solving four-order parabolic equation Ul+Uxxxx=0. The scheme meets a stability condition of r= △t/△x4<1/8 and shows a local truncation error of 0(△t2 + △x4 ).
In this paper,for a class of non-stiff problems,the convergence and stability of multistep Runge-Kutta methods are discussed and a prior bound of the global truncated error for this methods is presented.
Through the introduction of a reference atmosphere, prognostic variables become smoother on the tilted sigma-surface over mountains or a frontal zone, and thus truncation errors are reduced.
Truncation errors of selected finite difference methods for two-dimensional advection-diffusion equation with mixed derivatives
This paper presents the calculation of truncation errors, namely numerical diffusion and numerical dispersion for various finite difference schemes.
The effect of truncation errors is considered in the incremental virtual work equation.
Using a different method from , by analyzing the truncation errors of schemes, we give the sufficient conditions under which the solution of the difference scheme converges uniformly to the solution of the differential equation.
For the model to be computationally stable, the local truncation error of integration should be equal to 10-14 and the double precision of the Standard for Binary Floating-Point Arithmetic IEEE 754-1985 should be used.
The stability condition and local truncation error for the scheme are τ >amp;lt; 1/2 andO(Δt2 + Δx4 + Δy4 + Δz4), respectively.
The form is an expression for the local truncation error for a certain class of difference schemes.
By this term we mean meshes on which the local truncation error of the method is approximately constant in some norm.
Higher-order Runge-Kutta (RK) algorithms employing local truncation error (LTE) estimates have had very limited success in solving stiff differential equations.