Class HeatEquationSolver

java.lang.Object

org.episteme.core.mathematics.analysis.pde.HeatEquationSolver

public class HeatEquationSolver
extends Object

1D Heat Equation Solver. Supports Explicit and Implicit integration schemas.

Reference:
Fourier, J. (1822). Théorie analytique de la chaleur. Firmin Didot.

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
HeatEquationSolver(int nx, double length, double alpha)
HeatEquationSolver(int nx, Real length, Real alpha)

Method Summary

Modifier and Type	Method	Description
Real[]	getSolution()
void	setInitialCondition(Function<Real,Real> f)	Set initial condition.
void	setLeftBoundary(BoundaryType type, Real value)
void	setRightBoundary(BoundaryType type, Real value)
void	stepExplicit(Real dt)	Explicit Euler time step (FTCS scheme).
void	stepImplicit(Real dt)	Implicit Euler time step (unconditionally stable).

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

HeatEquationSolver

public HeatEquationSolver(int nx,
 Real length,
 Real alpha)

HeatEquationSolver

public HeatEquationSolver(int nx,
 double length,
 double alpha)

Method Details

setInitialCondition

public void setInitialCondition(Function<Real,Real> f)

Set initial condition.

setLeftBoundary

public void setLeftBoundary(BoundaryType type,
 Real value)

setRightBoundary

public void setRightBoundary(BoundaryType type,
 Real value)

stepExplicit

public void stepExplicit(Real dt)

Explicit Euler time step (FTCS scheme). Stable if dt invalid input: '<'= dx^2/(2*alpha)

stepImplicit

public void stepImplicit(Real dt)

Implicit Euler time step (unconditionally stable). Uses Thomas algorithm for tridiagonal system.

getSolution

public Real[] getSolution()