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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.
A box is 30 cm long, 8 cm wide and 12 cm high. Determine the length of the diagonal AB ? Round to the nearest tenth. a. 34.5 cm b. 32.1 cm c. 35.2 cm d. 33.3 cm
A radiograph is made of an object with a width of 3 mm using an x-ray tube with a 2 mm focal spot at a source-to-film distance of 100 cm. The object being imaged is 15 cm from the
I had just come back from a very interesting talk arranged by a Mathematics Centre, it was aimed at parents of primary school-going children. They had talked about, and demonstrate
Decision-Making Under Conditions of Uncertainty With decision making under uncertainty, the decision maker is aware of different possible states of nature, but has insufficient
Order to solve Mathematical Operations: Example: Solve the following equation: (4 - 2) + (3 x 4) - (10 ÷ 5) - 6 = ____________ Solution: a. Perform ma
Find out the number of ways in which 5 prizes can be distributed among 5 students such that (a) Each student may get a prize. (b) There is no restriction to the number o
2 of 10 =
solve for k such that the system 4x+ky=6 kx+y=-3
If α & ß are the zeroes of the polynomial 2x 2 - 4x + 5, then find the value of a.α 2 + ß 2 b. 1/ α + 1/ ß c. (α - ß) 2 d. 1/α 2 + 1/ß 2 e. α 3 + ß 3 (Ans:-1, 4/5 ,-6,
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