Package org.drip.fdm.definition

Class Diffusion1DPDE

java.lang.Object
org.drip.fdm.definition.SecondOrder1DPDE
org.drip.fdm.definition.Diffusion1DPDE
public class Diffusion1DPDE
extends SecondOrder1DPDE
Diffusion1DPDE implements the Evolution of R1 State Factor Space Response using the Diffusion PDE. The References are:

  • Datta, B. N. (2010): Numerical Linear Algebra and Applications 2nd Edition SIAM Philadelphia, PA
  • Cebeci, T. (2002): Convective Heat Transfer Horizon Publishing Hammond, IN
  • Crank, J., and P. Nicolson (1947): A Practical Method for Numerical Evaluation of Solutions of Partial Differential Equations of the Heat Conduction Type Proceedings of the Cambridge Philosophical Society 43 (1) 50-67
  • Thomas, J. W. (1995): Numerical Partial Differential Equations: Finite Difference Methods Springer-Verlag Berlin, Germany
  • Wikipedia (2023): Alternating-direction implicit method https://en.wikipedia.org/wiki/Alternating-direction_implicit_method
  • Wikipedia (2024): Crank–Nicolson method https://en.wikipedia.org/wiki/Crank%E2%80%93Nicolson_method




Author:
Lakshmi Krishnamurthy

  • Method Summary

    Modifier and Type Method Description
    static Diffusion1DPDE Standard​(R1ToR1 stateResponseFunction, RdToR1 diffusionFunction)
    Construct a Standard Instance of Diffusion1DPDE
    double timeDifferential​(double time, double factor)
    Compute the State Response Increment at the factor value and the time

    Methods inherited from class org.drip.fdm.definition.SecondOrder1DPDE

    stateResponseEvolutionFunction, stateResponseFunction

    Methods inherited from class java.lang.Object

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

  • Method Details

    • Standard

      public static final Diffusion1DPDE Standard​(R1ToR1 stateResponseFunction, RdToR1 diffusionFunction)
      Construct a Standard Instance of Diffusion1DPDE
      Parameters:
      stateResponseFunction - R1 to R1 State Response Function
      diffusionFunction - Rd to R1 Diffusion Function
      Returns:
      Standard Instance of Diffusion1DPDE

    • timeDifferential

      public double timeDifferential​(double time, double factor) throws java.lang.Exception
      Compute the State Response Increment at the factor value and the time
      Overrides:
      timeDifferential in class SecondOrder1DPDE
      Parameters:
      time - Time
      factor - Factor Space Value
      Returns:
      State Response Increment
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid