Assertion: y | /r/HasProperty | t
Facets:
Source sentences:
text: t n + 1 2 , {\displaystyle t=t_{n}+h/2={\tfrac {t_{n}+t_{n+1}}{2}},} the midpoint between t n {\displaystyle t_{n}} at which the value of y ( t ) {\displaystyle y(t)} is known and
text: t n + 1 {\displaystyle t_{n+1}} at which the value of y ( t ) {\displaystyle y(t)} needs to be found.
text: Instead, this tangent is estimated by using the original Euler's method to estimate the value of y ( t ) {\displaystyle y(t)} at the midpoint, then computing the slope of the tangent with f ( ) {\displaystyle f()} .
text: Note that the red chord is not exactly parallel to the green segment (the true tangent), due to the error in estimating the value of y ( t ) {\displaystyle y(t)} at the midpoint.
text: y ( t )
text: y ( t )
text: y ( t )
text: y ( t )
text: The implicit method (1i) is obtained by approximating the value at the half step t + h / 2 {\displaystyle t+h/2} by the midpoint of the line segment from y ( t )