Solvers of PDE (partial differential equations)

Migration to Java some part of C/C++ code from my math-library repository

Prerequisites

• JDK 21

Gradle isn't required because of embedded Gradle presence in the project

How to build

./gradlew clean build

Supported PD equation types

• Parabolic equation (described heat/mass transfer process):
  M(x,t,U)*dU_dt = dU( K(x,t,U)*dU_dx )_dx + V(x,t,U)*dU_dx + F(x,t,U) where U = U(x,t)
  Check ParabolicEquation for details

• Hyperbolic equation (described oscillation process):
  M(x,t,U)*d2U_dt2 + L(x,t,U)*dU_dt = dU( K(x,t,U)*dU_dx )_dx + V(x,t,U)*dU_dx + F(x,t,U) where U = U(x,t)
  Check HyperbolicEquation for details

Supported border conditions types

• Border condition type 1 (definite mode): U(X,t)
• Border condition type 2 (definite force): dU_dx(X,t)
• Border condition type 3 (elastic fixing): dU_dx(X,t) = h*(U(X,t) - Theta(t))

Solver

The finite-difference method was used, in result we get tridiagonal system of linear equations and solve it with help of tridiagonal matrix algorithm (or Thomas algorithm) (or "метод прогонки" in Russian).

Usage notes

Check solved problems in tests:

• Diffusion problem with type 1 of both border conditions
• Diffusion problem with type 2 of both border conditions
• Wave equation (plucked string) with type 1 of both border conditions