Question 10410 – Functions
March 16, 2024Question 10406 – Calculus
March 16, 2024Question 10263 – Calculus
Backward Euler method for solving the differential equation dy/dx = f(x,y) is specified by, (choose one of the following).
Correct Answer: B
Question 1 Explanation:
dy/dx = f(x,y)
With initial value y(x0) = y0. Here the function f and the initial data x0 and y0 are known. The function y depends on the real variable x and is unknown. A numerical method produces a sequence y0, y1, y2, ……. such that yn approximates y(x0 + nh) where h is called the step size.
→ The backward Euler method is helpful to compute the approximations i.e.,
yn+1 = yn + hf(x n+1, yn+1)
With initial value y(x0) = y0. Here the function f and the initial data x0 and y0 are known. The function y depends on the real variable x and is unknown. A numerical method produces a sequence y0, y1, y2, ……. such that yn approximates y(x0 + nh) where h is called the step size.
→ The backward Euler method is helpful to compute the approximations i.e.,
yn+1 = yn + hf(x n+1, yn+1)
yn+1 = yn + hf(xn, yn)
yn+1 = yn + hf(xn+1, yn+1)
yn+1 = yn-1 + 2hf(xn, yn)
yn+1 = (1 + h) f(xn+1, yn+1)
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