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<p>Many partial differential equations can be solved by converting into a pseudo-differential operator equation. But when the data is noisy, the numerical computation of the solution is unstable. In this work, we consider a modified fractional Tikhonov regularization scheme along with parameter choice rules for solving pseudo-differential operator equations. A better rate of convergence for this scheme is demonstrated along with the parameter choice rules. Several examples as well as numerical results are also discussed to illustrate the viability of the scheme.</p>

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A modified fractional Tikhonov regularization to solve the pseudo-differential operator equation

  • 期刊论文

  • 发表日期：

    2026年4月16日

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  • K. J. Sayana,
  • G. D. Reddy

摘要

Many partial differential equations can be solved by converting into a pseudo-differential operator equation. But when the data is noisy, the numerical computation of the solution is unstable. In this work, we consider a modified fractional Tikhonov regularization scheme along with parameter choice rules for solving pseudo-differential operator equations. A better rate of convergence for this scheme is demonstrated along with the parameter choice rules. Several examples as well as numerical results are also discussed to illustrate the viability of the scheme.