Question

A generalized numerical method for the initial value problemY′(x) =f(x,Y(x))Y(0) =Y0is given as:yn+1=yn+h[(1−θ)f(xn,yn) +θf(xn+1,yn+1)] (a) Show...

A generalized numerical method for the initial value problemY′(x) =f(x,Y(x))Y(0) =Y0is given as:yn+1=yn+h[(1−θ)f(xn,yn) +θf(xn+1,yn+1)]

(a) Show that the numerical method forθ=12is absolutely stable for the modeldifferential equation whenλ <0 .

(b) What is the region of absolute stabilty of the numerical method ifθ=13?

you can use

Elementary Numerical Analysis (3rd Edition)

as reference

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