Transcription of Systems of ODEs
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Systems of ODEs
New Mexico Tech Hyd 510 Hydrology Program Quantitative Methods in Hydrology 154 Systems of ODEs Chapter 4 your textbook introduces Systems of first order ODES. In general, these can be represented by the matrix expression y =f(t,y), where y = {y1 , y2, y3, .., yn-1, yn}T is a column vector of unknows, t is a scalar independent variable, and the prime indicates differentiation wrt to t. Typically for us the independent variable t is time. This can also be written as shown below, taken from p. 134 ( ) of the text: on a t b that satisfy (1) on this interval. In vector form y=h(t) = {h1 , h2, h3, .., hn-1, hn}T. An initial value problem for (1) consists of (1) and n ICs y1(t0)= K1, y2(t0)= K2, y3(t0)= K3, , .., yn(t0)= Kn, where the K s are constants, or y(t0)=K = {K1, K2, K 3, .., K n-1, K n}T . In all cases that you will see in hydrology, Systems of equations, like that in (1) are IVPs (after all, it is a system of 1st order ODEs).
Systems of ODEs Chapter 4 your textbook introduces systems of first order ODES. In general, these can be represented by the matrix expression y’=f(t,y), where y = {y1, y2, y3, …, yn-1, yn} T is a column vector of unknows, t is a scalar independent variable, and the prime indicates differentiation wrt to t. Typically
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