Article ID Journal Published Year Pages File Type
1140798 Mathematics and Computers in Simulation 2006 18 Pages PDF
Abstract

The following multiple integral is involved in the neutron star theory:τ(ε,v)=1ω(ε)∫0π/2dθsin⁡(θ)∫0∞dnn2∫0∞dph(n,p,θ,ε,v)whereh(n,p,θ,ε,v)=ψ(z)ϕ(n−ε−z)+ψ(−z)ϕ(n−ε+z)−ψ(z)ϕ(n+ε−z)−ψ(z)ϕ(n+ε+z)h(n,p,θ,ε,v)=ψ(z)ϕ(n−ε−z)+ψ(−z)ϕ(n−ε+z)−ψ(z)ϕ(n+ε−z)−ψ(z)ϕ(n+ε+z)andz=p2+(vsin⁡(θ))2,ψ(x)=1exp⁡x+1,ϕ(x)=xexp⁡x−1.ω(ε)ω(ε) is a normalization function.The aim is to get a table for τ(ε,v)τ(ε,v) for some values of (ε,v)(ε,v) in [10−4,104]×[10−4,103][10−4,104]×[10−4,103] and then to interpolate for the others. We present a new strategy, using the Gauss–Legendre quadrature formula, which allows to have one code available whatever the values of vv and εε are. We guarantee the accuracy of the final result including both the truncation error and the round-off error using Discrete Stochastic Arithmetic.

Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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