What question did this study set out to answer?

The aim is to improve the computational efficiency and accuracy of solving the 2D heat conduction equation.

March 14, 2026MathematicsOpen Access

Fourth-Order Compact Finite-Difference Scheme with Discrete Sine Transform for Solving 2D Heat Conduction Equation with DBCs

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Numerical experiments demonstrate reduced computational cost for solving heat conduction equations in large grids using a discrete sine transform.

The aim is to improve the computational efficiency and accuracy of solving the 2D heat conduction equation.
Proposed a hybrid technique combining a fourth-order finite-difference approach with discrete sine transform
Evaluated the method on large grids with homogeneous Dirichlet boundary conditions
Conducted detailed numerical experiments using MATLAB R2024b
Achieved substantial reductions in computational cost
Maintained high numerical accuracy in solving heat conduction equations

Liu et al. (2026) studied this question.

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Numerical experiments demonstrate reduced computational cost for solving heat conduction equations in large grids using a discrete sine transform.