What question did this study set out to answer?

The research aims to identify two time-dependent coefficients in a second-order parabolic equation under nonlocal conditions.

April 5, 2026F1000ResearchOpen Access

Simultaneous Numerical Determination of Two Time-dependent Coefficients in Second Order Parabolic Equation With Nonlocal Initial and Boundary Conditions

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Mathematical framework identifies coefficients in parabolic equations, suggesting improved stability and accuracy for applications.

The research aims to identify two time-dependent coefficients in a second-order parabolic equation under nonlocal conditions.
Utilized the Crank-Nicolson finite difference method for solving the direct problem.
Reformulated the inverse problem as a nonlinear regularized least-squares optimization problem.
Employed Tikhonov regularization to enhance numerical stability and robustness.
Performed extensive numerical experiments to assess accuracy and convergence.”],
results
: [
Regularization effectively minimizes reconstruction error and dampens numerical oscillations.
The methodology is validated through experiments using both exact and noisy data.
Sensitivity analysis highlights the importance of the regularization parameter for stability versus accuracy trade-off.
Regularization effectively minimizes reconstruction error and dampens numerical oscillations.
The methodology is validated through experiments using both exact and noisy data.
Sensitivity analysis highlights the importance of the regularization parameter for stability versus accuracy trade-off.

A.J.Al-Shatrah et al. (2026) studied this question.

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