We develop continuous-stage Runge-Kutta methods based on weighted orthogonal polynomials in this paper. There are two main highlighted merits for developing such methods: Firstly, we do not need to study the tedious s...
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In this paper, we study symplectic integration of canonical Hamiltonian systems with Jacobi polynomials. The relevant theoretical results of continuous-stage Runge-Kutta methods are revisited firstly and then symplect...
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We propose an extended framework for continuous-stage Runge-Kutta methods which enables us to treat more complicated cases especially for the case weighting on infinite intervals. By doing this, various types of weigh...
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As is well known, energy is generally deemed as one of the most important physical invariants in many conservative problems and hence it is of remarkable interest to consider numerical methods which are able to preser...
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Let F2m be a finite field of cardinality 2m, λ and k be integers satisfying λ, k ≥ 2 and denote R = F2m[u]/hu2λ. Let δ, α ∞ F2m. For any odd positive integer n, we give an explicit representation and enumeratio...
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Let p be an odd prime number, Fpm be a finite field of cardinality pm and s a positive integer. Using some combinatorial identities, we obtain certain properties for Kronecker product of matrices over Fp with a specif...
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Let F2m be a finite field of cardinality 2m, R = F2m + uF2m (u2 = 0) and s, n be positive integers such that n is odd. In this paper, we give an explicit representation for every self-dual cyclic code over the finite ...
The main purpose of this paper is to investigate the properties of a mapping which is required to be roughly bilipschitz with respect to the Apollonian metric (roughly Apollonian bilipschitz) of its domain. We prove t...
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