b) Use modified Euler’s method to find the approximate solution of IVP
at
with
If the exact solution is find the error.
Solve Numerically --
b) Use ___ _______ _______ _________ ________ ______ _________.
________ ___ ___ ____ _____ __________ __________ ____ _____ ____.
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b) i) Calculate the third-degree Taylor polynomial abou for
ii) Use the polynomial in part (i) to approximate and find a bound for the error involved.
iii) Use the polynomial in part (i) to approximate
a) Solve the system of equations
by LU decomposition method and find the inverse of the coefficient matrix
Take 10 figure logarithm to bases 10 from to
by unit increment. Calculate the first derivative of
when
c) Show that is a solution of the difference equation
a) Derive a suitable numerical differentiation formula of to find
with
given the table
| x | 0.1 | 1.2 | 2.4 | 3.9 |
| f(x) | 3.41 | 2.68 | 1.37 | -1.48 |
a) Determine the constants in the differentiation formula
so that the method is of the highest possible order. Find the order and the error term of the method.
b) Use modified Euler’s method to find the approximate solution of IVP
at
with
If the exact solution is find the error.