{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

22 maximum pointwise errors in the solution of

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: vely. The implementation of the collocation scheme is usually done by eliminating the unknowns k , k = 1 2 : : : J , appearing in (9.2.7b) on each subinterval and then solving for the nodal values Y = Y(x ), i = 0 1 : : : N . We'll illustrate this for a linear system ; ; ; ik i i f (x y) = A(x)y + b(x) g (y(a)) = Ly(a) ; l g (y(b)) = Ry(b) ; r: L R 18 (9.2.8a) (9.2.8b) Nonlinear problems are solved using Newton's method to linearize them to the form of (9.2.8). For a linear problem, (9.2.7b) becomes k = A( ) Y 1 + h ik ik i; X J i j =1 a k ] + b( ) kj ij k = 1 2 : : : J: ik (9.2.9a) This system can be written in matrix form as Wk =VY 1+q i where 2 a A( 6 a12 11A( W = I;h 6 6 ... 4 i i i i i; (9.2.9b) i a1 2 A( 1) a2 2 A( 2) 1) 2) a1 A( 1) a2 A( 2) i J i ... ... ... a 1 A( ) a 2 A ( ) a A( ) i J 2k 3 6 k 12 7 k = 6 .. 7 6.7 45 i iJ J J iJ i (9.2.9c) iJ i i i i i A( ) iJ 3 7 7 7 5 2 b( ) 3 6 b( 12) 7 q = 6 .. 7 : 6.7 4 5 i i i JJ 2 A( ) 3 6 A( 12) 7 V = 6 .. 7 6.7 4 5 i k i (9.2.9d) b( ) iJ iJ Let us write (9.2.7a) in the form Y = Y 1 + h Dk i where i; i 2bI 6 1 b2I D=6 6 4 ... (9.2.10a) i bI 3 7 7:...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern