PROGRAM DESCRIPTION:

The program uses Euler's Method for approximating a first-order Differential Equation. Given the differential equation Y', a step value h,and a domain from X0 to X1, my application calculates a numerical solution to the differential equation at the end domain, and every step point between the start and end of the domain.

% ERROR IN EULERS METHOD:

While my program accounts for much floating-point arithmetic errors and rounding errors, the user must be aware of discretization error and rounding error tradeoff. Outisde of the very small rounding the computer may do naturally, Eulers method's % error is dependent on the choice of step. Essentially, the bigger your step, the higher your % error will be. However, the smaller your step, the more steps will have to be computed. I.E, your step is proportional to your discretization error, and inversely proportional to the number of computations(and thus the number of times a rounding error may occur). As such, it is up to the user to experiment and choose a proper step value for h.

LIMITATIONS:

Currently, this program supports the following functions:

sin, cos, tan,

asin, acos, atan,

sinh, cosh, coth,

asinh, acosh, acoth,

sec, csc, cot,

asec, acsc, acot,

sech, csch, coth,

asech, acsch, acoth,

sqrt, ln, log, abs

Currently 28 functions total.

(for logs that dont conform to logbase10 or ln, use change of base formula before inputting)

TO ENSURE ACCURATE RESULTS:

-Enter the problem in its most reduced form. In the current version, the calculator can't catch edge cases where a function may reduce via division, and can produce a dividing by zero error. E.G: (y^2)/y where y = 0 will produce an error.

-Enter functions with the term they're being applied to in parentheses. E.G: Sin(12x-2) or cos(2x), not cosx

-Functions are to be typed in lowercase. sin, cos, tan, etc.

-exponentiation of functions is to be denoted as (sin(x))^2, NOT sin^2(x), to avoid ambiguity.

-enter inverse trig as asin, acos, etc.. not arcsin or sin^-1

-Decimals should be entered as 0.123, not .123

-Note that this program does not support factorials or complex values in the current version.