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30 - Solving IVPs

# 30 - Solving IVPs - Scalar problems Systems of ODEs...

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Unformatted text preview: Scalar problems Systems of ODEs Stiffness Solving IVPs Dhavide Aruliah UOIT MATH 2070U c D. Aruliah (UOIT) Solving IVPs MATH 2070U 1 / 15 Scalar problems Systems of ODEs Stiffness Solving IVPs 1 Scalar problems 2 Systems of ODEs 3 Stiffness c D. Aruliah (UOIT) Solving IVPs MATH 2070U 2 / 15 Scalar problems Systems of ODEs Stiffness Some scalar test problems to try ODEs with initial condition y ( ) = 1 ODE y = f ( t , y ) Solution y = y ( t ) = 1 y = t y ( t ) = 1 + t 2 /2 y = y y ( t ) = e t y =- y y ( t ) = e- t y = 1/ ( 1- 3 t ) y = 1- ( 1/3 ) ln ( 1- 3 t ) y = 2 y- y 2 y = 2/ ( 1 + e- 2 t ) Use ode23 to generate numerical solutions to all of the above c D. Aruliah (UOIT) Solving IVPs MATH 2070U 4 / 15 Scalar problems Systems of ODEs Stiffness tspan = [0 10]; % interval of integration y0 = 1; % initial condition F1 = @(t,y) 0; % zero function ode23( F1, tspan, y0 ) % exact soln y=1 F2 = @(t,y) t; ode23( F2, tspan, y0 ) % exact soln y=1+t^2/2 F3 = @(t,y) y; ode23( F3, tspan, y0 ) % exact soln y=exp(t) c D. Aruliah (UOIT) Solving IVPs MATH 2070U 5 / 15 Scalar problems Systems of ODEs Stiffness M ATLAB IVP solvers To solve IVP y = f ( t , y ) subject to y ( ) = y with MATLAB: I Generate function f to represent function f ( t ,...
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30 - Solving IVPs - Scalar problems Systems of ODEs...

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