A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems

Algorithm 1

The Chebyshev series method of order with constant matrix .

Input:  % Insert the initial values of the vectors and ,

% Define both the step size and the number of iteration ;

% Define the Chebyshev polynomials at the endpoints of the interval , that is and

for acceding to Eq. (11)

% Define at for and acceding to

Eq. (13).

for

;

%Define the successive derivatives of the solution vector according to Eq. (18).

for

end

% If we refer to the derivative of the Chebyshev coefficient by , as an

example, the recurrence relation (19) can be used to estimate the successive values of the

Chebyshev coefficient vectors with a reverse order as follows:

;

;

;

;

;

;

end

% Equation (21) is used to estimate the remaining coefficient .

;

for  

;

end

% Substitute by the estimated coefficients into Eq. (15) to get the required approximation at

the end of the integration step.

;

for  

;

end

;

end