Title: A fuzzy component technique for 3D convection-diffusion equation based on compact discretisation and exponential basis

Authors: Navnit Jha; Kritika; Shivani Khandol

Addresses: Department of Mathematics, South Asian University, Rajpur Road, New Delhi – 110068, India ' Department of Mathematics, South Asian University, Rajpur Road, New Delhi – 110068, India ' Department of Mathematics, South Asian University, Rajpur Road, New Delhi – 110068, India

Abstract: This study introduces a fourth-order fuzzy component numerical technique incorporating compact discretisation, an exponential basis and fuzzy transform to solve 3D convection-diffusion equations. The proposed technique approximates the fuzzy components of the source function and solution representing mass transfer with an algebraic combination of seven and nineteen points respectively. This technique computes fourth-order accurate numerical solutions in the optimal time frame. The function approximation by fuzzy transform is estimated on an exponential basis, requiring the evaluation of free parameters. The value of free parameters is obtained in such a manner that the numerical scheme achieves sixth-order local truncation errors. This configuration yields a block tridiagonal matrix that optimises computation time and reduces the memory cost. By adjusting frequency parameters present on an exponential basis, an optimised numerical solution can be determined. The performance of the proposed technique is evaluated using a variety of convection-diffusion equations, along with the sine-Gordon equation. The technique's usefulness and efficiency are demonstrated by error bounds and their convergence order.

Keywords: numerical computation; elliptic partial differential equation; fuzzy transform; triangular membership function; sine-Gordon equation; convection-diffusion equation; maximum absolute error.

DOI: 10.1504/IJANS.2025.151201

International Journal of Applied Nonlinear Science, 2025 Vol.5 No.2, pp.132 - 151

Received: 31 Aug 2024
Accepted: 15 Oct 2024
Published online: 19 Jan 2026 *

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