MATH 475B Lecture Notes - Lecture 2: Jacobian Matrix And Determinant, Numerical Method
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Page 1 of 5 - jan 18, 2011. This gives us a way to solve for the y(t+h) in terms of y(t) via an implicit equation. Newton"s method: linearize equation, solve linearized equation, then readjust and solve again. Problems: could be zero of fail to be invertible (respectively). The derivative in the scalar case or the jacobian matrix. Can show if guess is close enough to actual answer, then the solution converges to the actual value. Page 2 of 5 - jan 18, 2011. Numerical method for solving this to implement backward euler is. We have an advantage in this setting as we can use y(t) as our initial guess for the y(t+h) unknown. (because usually the biggest problem in newton"s method is nding the initial guess) Forward euler is explicit, no newtons method needed. Have problems with stiff differential equations, much more expensive to solve using explicit than implicit solvers.