test_ode – Numerical Methods

Uses

- ode
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Graph Key

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Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.

Program to test the ode module. The Lorenz chaotic system is solved: $\frac{dx}{dt}= a\left(y-x\right)\\ \frac{dy}{dt}= x\left(b-z\right) - y \\ \frac{dz}{dt}= xy - cz$ The system is integrated for $t\in[0,10]$ with $a=$ , $b=$ and $c=$ . For initial conditions $\left(x(0),y(0),z(0)\right) = \left(1,1,1\right)$ , the solution is: Image of the trayectory

Calls

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Variables

Type	Attributes		Name		Initial
integer,	parameter	::	N	=	1000
real		::	Tf
real		::	dT
real		::	t(0:N)
real		::	U(0:N,3)
real		::	U0(3)
integer		::	i
integer		::	file_unit

Functions

function lorenz(U, t) result(dU)

function for defining derivative in the Lorenz system written as: $\frac{d\mathbf{U}}{dt}=\mathbf{F}\left(\mathbf{U},t\right)$ where: $\mathbf{U}\left(t\right) = \begin{pmatrix} x\left(t\right)\\ y\left(t\right)\\ z\left(t\right) \end{pmatrix}$ and $\mathbf{F}\left(\mathbf{U},t\right)= \begin{pmatrix} a \left( U_2 - U_1 \right) \\ U_1 \left( b - U_3 \right) - U_2 \\ U_1 U_2 - cU_3 \end{pmatrix}$

Arguments

Type	Intent	Optional	Attributes		Name
real,	intent(in)			::	U(:)
real,	intent(in)			::	t

test_ode Program

Contents

Variables

Functions

Uses

Calls

Variables

Functions

function lorenz(U, t) result(dU)

Arguments

Return Value real, (size(U))