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<p><?tk 4?>An innovative sixth algebraic order technique of the Adams-Bashforth-Moulton predictor–corrector–corrector type is introduced in this paper. The innovative method allows for the accurate integration of any set of functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\left[ 1, \, x, \, x^2, \, x^3, \, x^4, \, e^{I\, v \, x}\right]\)</EquationSource> </InlineEquation>. The new method’s stability zones have been drawn. This new approach was used in quantum chemistry to solve the difficult Schrödinger-type coupled differential equations problem. Other related problems are also addressed with the novel method.</p>

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New predictor–corrector–corrector method for the approximation of the Schrödinger equation and related problems

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Rubayyi T. Alqahtani,
  • Theodore E. Simos

摘要

An innovative sixth algebraic order technique of the Adams-Bashforth-Moulton predictor–corrector–corrector type is introduced in this paper. The innovative method allows for the accurate integration of any set of functions \(\left[ 1, \, x, \, x^2, \, x^3, \, x^4, \, e^{I\, v \, x}\right]\) . The new method’s stability zones have been drawn. This new approach was used in quantum chemistry to solve the difficult Schrödinger-type coupled differential equations problem. Other related problems are also addressed with the novel method.