CHEN 3201 Lecture Notes - Lecture 31: Numerical Stability, Backward Euler Method, Euler Method

• School: UMN
• Department: Chemical Engineering
• Course: CHEN 3201
• Professor: Kevin Dorfman

Document Summary

Explicit euler define next term with previous term and derivative of it called explicit b/c we know everything on right hand side of eqn and we use it to solve for left hand side. Implicit euler don"t know and left hand side solve using newton"s method if you have numerical instability, then use the implicit euler. Rk2 = predictor corrector method error here is proportional to h2. Chen3201_numericalmethods page 2 function recitation08 t = 0; y = 1; h = 0. 1; nsteps = 100; T(1) = t; for i = 1:nsteps y=rk4(y,t,h); t=t+h; Now solving the same problem using implicit euler. -> so we know that there was nothing wrong with the explicit methodit"s just a problem with our function itself. If make more steps, then rk blows up but implicit gives some value. Chen3201_numericalmethods page 5 in matlab, to calculate error e = getr(y_new,y_old,