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As noted, Euler's method is little used in practice, as there are much better ways of solving initial value problems. By better, we mean, "able to achieve a result of the same precision using a larger step size". [Euler's method is also unstable for some problems where the step size can take you outside the physical domain of the function and the solution runs away to infinity.]
To improve on Euler's method, we will use the fourth-order Runge-Kutta method. This method requires four evaluations of the differential at each step, but often allows a much larger step size to achieve the same result. The method can be summarised as:
where we have written h in place of the step size Δx.
Find the sum of (1 - 1/n ) + (1 - 2/n ) + (1 - 3/n ) ....... upto n terms. Ans: (1 - 1/n ) + (1 - 2/n ) - upto n terms ⇒[1+1+.......+n terms] - [ 1/n + 2/n +....+
Every point (x,y) on the curve y=log2 3x is transferred to a new point by the following translation (x',y')=(x+m,y+n), where m and n are integers. The set of (x',y') form the curve
The distance from the earth to the moon is approximately 240,000 miles. What is this distance expressed in scientific notation? To convert to scienti?c notation, place a decima
triangular with base AB = 48cm and height CH=16cm is inscribed a rectangle MNPQ in which MN: MQ = 9:5 Find MN and MQ
The line 4x-3y=-12 is tangent at the point (-3,0) and the line 3x+4y=16 is tangent at the point (4,1). find the equation of the circle. solution) well you could first find the ra
I cant figure out how to study for my math test
Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
Rates of Change and Tangent Lines : In this section we will study two fairly important problems in the study of calculus. There are two cause for looking at these problems now.
Factor following. x 2 - 20 x + 100 Solution In this case we've got three terms & it's a quadratic polynomial. Notice down as well that the constant
What is a two step equation that equals 8 ?
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