An averaging method for the stiff highly oscillatory problem

An Averaging Technique for Highly Oscillatory Hamiltonian Problems

In this paper, we are concerned with the numerical solution of highly-oscillatory Hamiltonian systems with a stiff linear part. We construct an averaged system whose solution remains close to the exact one over bounded time intervals, possesses the same adiabatic and Hamiltonian invariants as the original system, and is non-stiff. We then investigate its numerical approximation through a method...

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.

Extended defect corrected averaging for highly oscillatory PDEs

We consider parabolic partial differential equations where the support of the sources or of the inhomogenous Neumann boundary conditions undergoes an oscillatory motion. The timescale of this oscillation is much smaller than the characteristic time scale of diffusion, which is of main interest. Resolution of the smallest timescale constitutes a strong restriction on the stepsize of time integra...

An Asymptotic Parallel-in-Time Method for Highly Oscillatory PDEs

An Efficient Method for Computing Highly Oscillatory Physical Optics Integral

Abstract—In this work, we use the numerical steepest descent path (numerical SDP) method in complex analysis theory to calculate the highly oscillatory physical optics (PO) integral with quadratic phase and amplitude variations on the triangular patch. The Stokes’ phenomenon will occur due to various asymptotic behaviors on different domains. The stationary phase point contributions are careful...