Question

Given v' = 1+2.y(0) = 0, y(0.2) – 0.2027. y(0.4) = 0.4228, y(0.6) = 0.6841,
the predictor value y(0.8) using Milne's method is​

Answer 1

Answer:

1.0303

Explanation:

Milne's Method: For systems of first-order ordinary differential equations, the Cauchy problem can be solved using the finite-difference approach. Y(a)=b and y′=f(x,y)By using Milne's method, the predictor value y(0.8) is equal to 1.0303

• The "Milne approach" here is known as the (explicit) midpoint rule in Western literature.
• The corrector that appears in the "predictor-corrector Milne approach" is instead referred to as a Milne device or a Milne method.
• The Simpson quadrature rule is directly applied to differential equations using this technique.
• Dahlquist stability is a word that is no longer often used in English literature. One uses "zero-stabilizers-stability," "root-stability root-stability," or simply "stability" more commonly.

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