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scalation/scalation/scalation.dynamics/scalation.dynamics.pde

scalation.dynamics.pde

package scalation.dynamics.pde

Members list

Type members

Classlikes

class FirstOrderPDE(v: (Double, Double) => Double, dt: Double, dx: Double, xm: Double, ic: FunctionS2S, bc: (Double, Double), f: (Double, Double) => Double = ...)

The FirstOrderPDE class is used to solve First Order Partial Differential Equations like the Advection Equation. Let 'u(x, t)' = concentration in a fluid with velocity 'v' at position '0 <= x <= xm' and time 't' > 0. Numerically solve the

The FirstOrderPDE class is used to solve First Order Partial Differential Equations like the Advection Equation. Let 'u(x, t)' = concentration in a fluid with velocity 'v' at position '0 <= x <= xm' and time 't' > 0. Numerically solve the

Advection Equation: u_t + v(x, t) u_x = 0 ∂u/∂t + v(x, t) ∂u/∂x = 0 with initial conditions u(x, 0) = ic(x) boundary conditions (u(0, t), u(xm, t)) = bc

Value parameters

bc

the boundary conditions as a 2-tuple for end-points 0 and 'xm'

dt

delta 't'

dx

delta 'x'

f

the flux (how much flow) function f(u, x)

ic

the initial conditions as a function of position 'x'

v

the velocity field function v(x, t)

xm

the length of the column

Attributes

Supertypes
class Object
trait Matchable
class Any
class ParabolicPDE(k: Double, dt: Double, dx: Double, xm: Double, ic: FunctionS2S, bc: (Double, Double))

The ParabolicPDE class is used to solve parabolic partial differential equations like the Heat Equation. Let 'u(x, t)' = temperature of a rod at position '0 <= x <= xm' and time 't' > 0. Numerically solve the

The ParabolicPDE class is used to solve parabolic partial differential equations like the Heat Equation. Let 'u(x, t)' = temperature of a rod at position '0 <= x <= xm' and time 't' > 0. Numerically solve the

Heat Equation: u_t = k u_xx ∂u/∂t = k ∂^2u/∂^2x with initial conditions u(x, 0) = ic(x) boundary conditions (u(0, t), u(xm, t)) = bc

Value parameters

bc

the boundary conditions as a 2-tuple for end-points 0 and 'xm'

dt

delta 't'

dx

delta 'x'

ic

the initial conditions as a function of position 'x'

k

the thermal conductivity/diffusion constant

xm

the length of the rod

Attributes

Supertypes
class Object
trait Matchable
class Any
final class firstOrderPDETest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class firstOrderPDETest2

Attributes

Supertypes
class Object
trait Matchable
class Any
final class firstOrderPDETest3

Attributes

Supertypes
class Object
trait Matchable
class Any
final class firstOrderPDETest4

Attributes

Supertypes
class Object
trait Matchable
class Any
final class parabolicPDETest

Attributes

Supertypes
class Object
trait Matchable
class Any
final class parabolicPDETest2

Attributes

Supertypes
class Object
trait Matchable
class Any

Value members

Concrete methods

def firstOrderPDETest(): Unit

The firstOrderPDETest main function is used to test the FirstOrderPDE class. Numerically solve the Advection Equation: '∂u/∂t + v(x, t) * ∂u/∂x = 0'

The firstOrderPDETest main function is used to test the FirstOrderPDE class. Numerically solve the Advection Equation: '∂u/∂t + v(x, t) * ∂u/∂x = 0'

runMain scalation.dynamics.pde.firstOrderPDETest

Attributes

def firstOrderPDETest2(): Unit

The firstOrderPDETest2 main function is used to test the FirstOrderPDE class. Numerically solve the Advection Equation: '∂u/∂t + v(x, t) * ∂u/∂x = 0'

The firstOrderPDETest2 main function is used to test the FirstOrderPDE class. Numerically solve the Advection Equation: '∂u/∂t + v(x, t) * ∂u/∂x = 0'

runMain scalation.dynamics.pde.firstOrderPDETest2

Attributes

def firstOrderPDETest3(): Unit

The firstOrderPDETest3 main function is used to test the FirstOrderPDE class. Numerically solve the Advection Equation: '∂u/∂t + v(x, t) * ∂u/∂x = 0'

The firstOrderPDETest3 main function is used to test the FirstOrderPDE class. Numerically solve the Advection Equation: '∂u/∂t + v(x, t) * ∂u/∂x = 0'

Attributes

See also

www.public.asu.edu/~hhuang38/pde_slides_numerical.pdf

runMain scalation.dynamics.pde.firstOrderPDETest3

def firstOrderPDETest4(): Unit

The firstOrderPDETest4 main function is used to test the FirstOrderPDE class. Numerically solve the Burgers' Equation: ∂u/∂t + ∂f(u)/∂x = 0 with Flux Function: f(u) = 0.5 u^2 by the Chain Rule: ∂u/∂t + u ∂u/∂x = 0

The firstOrderPDETest4 main function is used to test the FirstOrderPDE class. Numerically solve the Burgers' Equation: ∂u/∂t + ∂f(u)/∂x = 0 with Flux Function: f(u) = 0.5 u^2 by the Chain Rule: ∂u/∂t + u ∂u/∂x = 0

Attributes

See also
def parabolicPDETest(): Unit

The parabolicPDETest main function is used to test the ParabolicPDE class. Numerically solve the Heat Equation: ∂u/∂t = k ∂^2u/∂x^2. Modeling the flow of heat in a rod.

The parabolicPDETest main function is used to test the ParabolicPDE class. Numerically solve the Heat Equation: ∂u/∂t = k ∂^2u/∂x^2. Modeling the flow of heat in a rod.

Attributes

See also

personales.unican.es/gutierjm/cursos/cornell/9_PDEs.pdf

runMain scalation.dynamics.pde.parabolicPDETest

def parabolicPDETest2(): Unit

The parabolicPDETest main function is used to test the ParabolicPDE class. Numerically solve the Diffusion Equation: ∂u/∂t = d ∂^2u/∂x^2. Modeling the spread of dye in a pipe.

The parabolicPDETest main function is used to test the ParabolicPDE class. Numerically solve the Diffusion Equation: ∂u/∂t = d ∂^2u/∂x^2. Modeling the spread of dye in a pipe.

Attributes

See also

runMain scalation.dynamics.pde.parabolicPDETest2

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