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- W2562853831 abstract "Structure preserving and structure exploiting iterative methods have recently recieved considerable interest in the numerical linear algebra community; see e.g., [1]. Exponential integrators that use Krylov approximations of matrix functions have turned out to be efficient for the timeintegration of certain ordinary differential equations (ODEs). In this result we will propose a new stucture exploiting iterative method based on an Arnoldi method and exponential integrators to solve certain types of ODEs. We consider linear stiff inhomogeneous ODEs, y′(t) = Ay(t) + g(t), where the function g(t) is assumed to satisfy certain regularity conditions. We derive an algorithm for this problem which is equivalent to Arnoldi’s method. The construction is based on expressing the function g(t) as a linear combination of given basis functions [φi]i=0 with particular properties. The properties are such that the inhomogeneous ODE can be restated as an infinite-dimensional linear homogeneous ODE. Moreover, the linear homogeneous infinite-dimensional ODE has properties that allow us to directly extend a Krylov method for finite-dimensional ODEs. Although the construction is based on an infinite-dimensional operator, the algorithm can be carried out with operations involving matrices and vectors of finite size. This type of construction resembles in many ways the infinite Arnoldi method, for nonlinear eigenvalue problem [2]. We prove convergence of the algorithm under certain natural conditions, and illustrate properties of the algorithm with examples stemming from the discretization of partial differential equations." @default.
- W2562853831 created "2017-01-06" @default.
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- W2562853831 date "2015-01-01" @default.
- W2562853831 modified "2023-10-03" @default.
- W2562853831 title "A structure exploiting infinite Arnoldi exponential integrator for linear inhomogeneous ODEs" @default.
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- W2562853831 hasPublicationYear "2015" @default.
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