diffq-algorithms+ - Algorithms for solving some...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

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

Unformatted text preview: Algorithms for solving some differential equations Jonathan L.F. King University of Florida, Gainesville FL 32611-2082, USA squash@math.ufl.edu Webpage http://www.math.ufl.edu/ squash/ 11 February, 2009 (at 12:49 ) Abstract: Gives a general method for writing the solution to a f irst-o rder l inear d ifferential e quation in terms of definite integrals. Step F1 of The FOLDE algorithm Write the DE in the form d y d x + ( x ) y = g ( x ) . 1 : Pick ( i.e, compute ) an antiderivative of , ( x ) := Z ( x )d x. 2 : Finally, we store for later use the following two func- tions: e ( x ) = ... and 1 e ( x ) = ... . 3 : Step F2. Now define B ( x ) := e ( x ) g ( x ). Then compute an antiderivative, A ( x ) := Z B ( x )d x. Step F3. Now, for = anyconstant, the following definition of y will satisfy eq(1). y ( x ) := 1 e ( x ) 4 : Step F4. From eq(4), compute y . Plug in to eq (1) to see if your formula for y satisfies it. ( It is at this point that you will sometimes find that you have made a computa-...
View Full Document

Page1 / 2

diffq-algorithms+ - Algorithms for solving some...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online