Global integration of differential equations through Lobatto quadrature |
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Authors: | Owe Axelsson |
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Institution: | (1) Chalmers Institute of Technology, Gothenburg, Sweden |
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Abstract: | For the numerical solution of the initial value problemy=f(x,y), –1x1;y(–1)=y
0 a global integration method is derived and studied. The method goes as follows.At first the system of nonlinear equations is solved. The matrix (A
i,k
(n)
) of quadrature coefficients is nearly lower left triangular and the pointsx
k,n
,k=1,2,...,n are the zeros ofP
n
–P
n–2, whereP
n
is the Legendre polynomial of degreen. It is showed that the errors From the valuesf(x
i,n
,y
i,n
),i=1,2,...,n an approximation polynomial is constructed. The approximation is Chebyshevlike and the error at the end of the interval of integration is particularly small. |
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Keywords: | |
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