Optimal stability polynomials for numerical integration of initial value problems
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Numerical Mathematics Group
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AbstractWe consider the problem of finding optimally stable polynomial approximations to the exponential for application to one-step integration of initial value ordinary and partial differential equations. The objective is to find the largest stable step size and corresponding method for a given problem when the spectrum of the initial value problem is known. The problem is expressed in terms of a general least deviation feasibility problem. Its solution is obtained by a new fast, accurate, and robust algorithm based on convex optimization techniques. Global convergence of the algorithm is proven in the case that the order of approximation is one and in the case that the spectrum encloses a starlike region. Examples demonstrate the effectiveness of the proposed algorithm even when these conditions are not satisfied.
CitationOptimal stability polynomials for numerical integration of initial value problems 2012, 7 (2):247 Communications in Applied Mathematics and Computational Science
PublisherMathematical Sciences Publishers