) Using fourth order Taylor series method with , solve the initial value problem
upto .
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Check whether satisfies Lipschitz condition
i) on any rectangle and
;
ii) on any strip and
;
iii) on the entire plane.
Using standard five point formula, solve the Laplace equation in R where R is the square
subject to the boundary conditions
on
and
on
. Assume
.
Show that .
Show that
Using Runge-Kutta second order method with
(i) , (ii)
, solve the initial value problem
Upto . If the exact solution is
, obtain the error.
) Find the displacement u(x, t) of an infinite string using the method of Fourier transform given that the string is initially at rest and that the initial displacement is f(x), .
how that between every successive pair of zeros of J0(x) there exists a zero of J1(x).