Numerical solution of fourth-order stiff ordinary differential equations by implicit high order block backward differentiation formula

Asnor, Asma Izzati; Yatim, Siti Ainor Mohd; İbrahim, Zarina Bibi

doi:10.1063/5.0075591

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2024

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“…However, according to several researchers (see [1,13,14]) this technique has a drawback as it consumes a lot of computing time and human effort. Consequently, several researchers have turned their attention to direct integration methods for solving higher-order ODEs, as these methods have demonstrated features of accuracy and speed [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Nevertheless, all of the methods mentioned above are above are multistep.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Embedded Diagonally Implicit Methods for Directly Solving Fourth-order ODEs

Saleh,

Fawzi,

Hussain

et al. 2024

IHJPAS

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EDIRKTO, an Implicit Type Runge-Kutta Method of Diagonally Embedded pairs, is a novel approach presented in the paper that may be used to solve 4th-order ordinary differential equations of the form . There are two pairs of EDIRKTO, with three stages each: EDIRKTO4(3) and EDIRKTO5(4). The derivation techniques of the method indicate that the higher-order pair is more accurate, while the lower-order pair provides superior error estimates. Next, using these pairs as a basis, we developed variable step codes and applied them to a series of -order ODE problems. The numerical outcomes demonstrated how much more effective their approach is in reducing the quantity of function evaluations needed to resolve fourth-order ODE issues.

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