These questions are intended to be more challenging than those in Q(1)-(5). (a) The uniform error...

 

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These questions are intended to be more challenging than those in Q(1)-(5). (a) The uniform error is defined |x − x| 1 + |X| Show that this error converges to both the relative and absolute error in the appropriate limits, and state those limits. (b) Consider the ODE below F = dx dt show that the implicit Euler recurrence relation can be written Xn+1 =axn + b giving expressions for a and b. = 1 + tx [4 marks] These questions are intended to be more challenging than those in Q(1)-(5). (a) The uniform error is defined |x − x| 1 + |X| Show that this error converges to both the relative and absolute error in the appropriate limits, and state those limits. (b) Consider the ODE below F = dx dt show that the implicit Euler recurrence relation can be written Xn+1 =axn + b giving expressions for a and b. = 1 + tx [4 marks]

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Stepbystep solution for part a Show that the uniform error converges to both the relative and absolute error in the appropriate limits and state those ... View the full answer