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Methods for Periodic Initial Value Problems
, 2005
"... Pstable symmetric superimplicit methods for periodic initial value problems ..."
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Pstable symmetric superimplicit methods for periodic initial value problems
Complexity of Initial Value Problems
"... Abstract. How complex could the solution be to an initial value problem given by a polynomialtime computable function? This question can be given a natural and precise sense in computational complexity theory. In this note, we put together several results stating that more conditions on the problem ..."
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Abstract. How complex could the solution be to an initial value problem given by a polynomialtime computable function? This question can be given a natural and precise sense in computational complexity theory. In this note, we put together several results stating that more conditions
Bounds for Initial Value Problems 1
"... A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type: ..."
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A new method has been developed for finding rigorous upper and lower bounds to the solution of a wide class of initial value problems. The method is applicable to initial value problems of the following type:
The InitialValue Problem for . . .
"... Plane viscous channel flows are perturbed and the ensuing initialvalue problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this work offers a means whereby completely arbitrary initial input can be speci ed without having to re ..."
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Plane viscous channel flows are perturbed and the ensuing initialvalue problems are investigated in detail. Unlike traditional methods where traveling wave normal modes are assumed for solution, this work offers a means whereby completely arbitrary initial input can be speci ed without having
Consider the Initial Value Problem (IVP):
"... Abstract: New scheme for solving initial value problem of ordinary differential equation was derived. Starting from the general method of deriving the spline function, the scheme was developed based on interpolation and collocation. Key words: Initial value problems, ordinary differential equations, ..."
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Abstract: New scheme for solving initial value problem of ordinary differential equation was derived. Starting from the general method of deriving the spline function, the scheme was developed based on interpolation and collocation. Key words: Initial value problems, ordinary differential equations
On Global Error Estimation and Control for Initial Value Problems
, 2005
"... On global error estimation and control for initial value problems ..."
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Cited by 4 (0 self)
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On global error estimation and control for initial value problems
Symmetry analysis of initialvalue problems
"... Symmetry analysis is a powerful tool that enables the user to construct exact solutions of a given differential equation in a fairly systematic way. For this reason, the Lie point symmetry groups of most wellknown differential equations have been catalogued. It is widely believed that the set of ..."
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of symmetries of an initialvalue problem (or boundaryvalue problem) is a subset of the set of symmetries of the differential equation. The current paper demonstrates that this is untrue; indeed, an initialvalue problem may have no symmetries in common with the underlying differential equation. The paper also
Initial Value Problems
"... Abstract In the previous chapter we derived a simple finite difference method, namely the explicit Euler method, and we indicated how this can be analysed so that we can make statements concerning its stability and order of accuracy. If Euler’s method is used with constant time step h then it is con ..."
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then it is convergent with an error of order O(h) for all sufficiently smooth problems. Thus, if we integrate from 0 to 1 with step h = 10−5, we will need to perform 105 function evaluations to complete the integration and obtain a solution with error O(h). To achieve extra accuracy using this method we could reduce
Computational Complexity of Initial Value Problems
, 2008
"... We show, in answer to K. Ko’s question raised in 1983, that an initial value problem given by a polynomialtime computable, Lipschitz continuous function can have a polynomialspace complete solution. ..."
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We show, in answer to K. Ko’s question raised in 1983, that an initial value problem given by a polynomialtime computable, Lipschitz continuous function can have a polynomialspace complete solution.
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