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Numerical Methods

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Question 222

The pressure PPP (in kilopascals) at a specific depth in a hydraulic system is modelled by the equation

g(P)=P5+12P−8000 g(P) = P^5 + 12P - 8000 g(P)=P5+12P−8000
a.

Show that the equation g(P)=0g(P) = 0g(P)=0 has a root β\betaβ in the interval [6,7][6, 7][6,7].

[2]
b.

Using the iterative formula

Pn+1=8000−12Pn5withP1=6.2 P_{n+1} = \sqrt[5]{8000 - 12P_n} \quad \text{with} \quad P_1 = 6.2 Pn+1​=58000−12Pn​​withP1​=6.2

(i) Calculate the value of P2P_2P2​, giving your answer to 4 decimal places. (ii) By performing repeated iterations, find the value of β\betaβ to 4 decimal places.

[3]
Markscheme

Numerical Methods Questions

  1. A Level
  2. /Maths
  3. /Numerical Methods

329 exam-style questions on Edexcel A Level Maths Numerical Methods, covering 10.1 Locating Roots, 10.2 Iteration, 10.3 The Newton-Raphson Method, and 10.4 Applications to Modelling. Each one has a worked solution and a mark scheme showing where the marks go.

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