Linearized numerical schemes for the Boussinesq equation

Linearized numerical schemes for the Boussinesq equation

Two different linearized schemes are applied to a parametric finite-difference scheme concerning the numerical solution of the Boussinesq equation. At the first linearized scheme the nonlinear term of the equation is substituted by an appropriate value, while at the second scheme we use Taylor’s expansion. Both schemes are analyzed for local truncation error, stability and convergence. The resu...

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Geometric Numerical Schemes for the Kdv Equation

Geometric discretizations that preserve certain Hamiltonian structures at the discrete level has been proven to enhance the accuracy of numerical schemes. In particular, numerous symplectic and multi-symplectic schemes have been proposed to solve numerically the celebrated Korteweg-de Vries (KdV) equation. In this work, we show that geometrical schemes are as much robust and accurate as Fourier...

Comparison of Some Finite Difference Schemes for Boussinesq Paradigm Equation

On the Convergence of Numerical Schemes for the Boltzmann Equation

– We consider a time and spatial explicit discretisation scheme for the Boltzmannequation. We prove some Maxwellian bounds on the resulting approximated solution anddeduce its convergence using a new time-discrete averaging lemma.  2003 Éditions scientifiques et médicales Elsevier SAS MSC: 35A35; 65L20; 76PO5 RÉSUMÉ. – Nous considérons une discrétisation explicite en temps et espace de l’équat...