A general framework for solving Riemann–Hilbert problems numerically
نویسندگان
چکیده
منابع مشابه
A general framework for solving Riemann-Hilbert problems numerically
A new, numerical framework for the approximation of solutions to matrix-valued Riemann–Hilbert problems is developed, based on a recent method for the homogeneous Painlevé II Riemann–Hilbert problem. We demonstrate its effectiveness by computing solutions to other Painlevé transcendents. An implementation in Mathematica is made available online.
متن کاملA New Approach for Numerically Solving Nonlinear Eigensolution Problems
By considering a constraint on the energy profile, a new implicit approach is developed to solve nonlinear eigensolution problems. A corresponding minimax method is modified to numerically find eigensolutions in the order of their eigenvalues to a class of semilinear elliptic eigensolution problems from nonlinear optics and other nonlinear dispersive/diffusion systems. It turns out that the con...
متن کاملSolving linear generalized Nash equilibrium problems numerically
This paper considers the numerical solution of linear generalized Nash equilibrium problems. Since many methods for nonlinear problems require the nonsingularity of some second order derivative, standard convergence conditions are not satisfied in our linear case. We provide new convergence criteria for a potential reduction algorithm that allow its application to linear generalized Nash equili...
متن کاملAn approximate method for numerically solving fractional order optimal control problems of general form
In this article, we discuss fractional order optimal control problems (FOCPs) and their solutions by means of rational approximation. The methodology developed here allows us to solve a very large class of FOCPs (linear/nonlinear, time-invariant/time-variant, SISO/MIMO, state/input constrained, free terminal conditions etc.) by converting them into a general, rational form of optimal control pr...
متن کاملSolving Dirichlet problems numerically using the Feynman-Kac representation
In this paper we study numerical solutions of the Dirichlet problem in high dimensions using the Feynman-Kac representation. What is involved are Monte-Carlo simulations of stochastic differential equations and algorithms to accurately determine exit times and process values at the boundary. It is assumed that the radius of curvature of the boundary is much larger than the square root of the st...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Numerische Mathematik
سال: 2012
ISSN: 0029-599X,0945-3245
DOI: 10.1007/s00211-012-0459-7