TRAPEZOIDAL WITH NEWTON ITERATION ALGORITHM
2016-08-23
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* TO APPROXIMATE THE SOLUTION OF THE INITIAL VALUE PROBLEM:
* Y' = F(T,Y), A <= T <= B, Y(A) = ALPHA,
* AT (N+1) EQUALLY SPACED NUMBERS IN THE INTERVAL [A,B].
*
* INPUT: ENDPOINTS A,B; INITIAL CONDITION ALPHA; INTEGER N;
* TOLERANCE TOL; MAXIMUM NUMBER OF ITERATIONS M AT ANY ONE STEP.
*
* OUTPUT: APPROXIMATION W TO Y AT THE (N+1) VALUES OF T
* OR A MESSAGE OF FAILURE.
* Y' = F(T,Y), A <= T <= B, Y(A) = ALPHA,
* AT (N+1) EQUALLY SPACED NUMBERS IN THE INTERVAL [A,B].
*
* INPUT: ENDPOINTS A,B; INITIAL CONDITION ALPHA; INTEGER N;
* TOLERANCE TOL; MAXIMUM NUMBER OF ITERATIONS M AT ANY ONE STEP.
*
* OUTPUT: APPROXIMATION W TO Y AT THE (N+1) VALUES OF T
* OR A MESSAGE OF FAILURE.
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