Instructions to Candidates

Answer FOUR Questions

ANSWER(Purchase full paper to get all the solution) 

Q1)

a) Linear, homogeneous ODE, 3rd order, with variable coefficients

b)        Advantages:

1) The numerical solution works in the same easy way in cases where an analytical solution is difficult or not available (variable properties, complicated geometry and boundary conditions, non-linearity etc).

2) Easier to apply to discrete datasets.

Disadvantage: approximation (truncation) errors, which are controlled with better discretisation.

c) No solution can be calculated for both systems since their characteristic determinant is zero. No solution is possible for System 1 ([0] x [X]=[A] type). System 2 is indeterminate, having infinite solutions ([0] x [X]=[0] type, the equations are not linearly independent).

d) “You have missed something mate, your solution should consist of 3 terms C1-C3, since it is a 3rd order homogeneous ODE.”

e) An explicit solution allows the calculation of the unknown values in one calculation step (forward shooting), whereas the implicit scheme requires the solution of a linear system. Explicit solution schemes are only applied to initial value problems.

f) It can be true for Gauss elimination and Cramer’s rule, but the iteration methods can be demanding (many repetitions) even for a small system.

g) This is made specific by applying/satisfying the initial/boundary conditions. Homogeneous ODE: this is applied to the general solution of the homogeneous. Non-homogeneous ODE: this is applied to the complete general solution, after we add the particular solution for the RHS of the non-homogeneous.

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Last updated: Jun 23, 2021 11:03 AM