Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation Article Swipe

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Nizam G. Ghawadri , Norazak Senu , Firas A. Fawzi , Fudziah Ismail , Zarina Bibi İbrahim ·

YOU? · · 2018 · Open Access · · DOI: https://doi.org/10.3390/a12010010

In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods.

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Mathematics

Ode

Mathematical Analysis

Differential Equation

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Runge–Kutta methods Mathematics Ordinary differential equation Diagonal Ode Numerical methods for ordinary differential equations L-stability Type (biology) Explicit and implicit methods Mathematical analysis Set (abstract data type) Applied mathematics Differential equation Function (biology) Differential algebraic equation Geometry Computer science Ecology Biology Evolutionary biology Programming language

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Type: article
Language: en
Landing Page: https://doi.org/10.3390/a12010010
PDF: https://www.mdpi.com/1999-4893/12/1/10/pdf?version=1546079219
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Cited By: 15
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DOI: https://doi.org/10.3390/a12010010

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Title: Diagonally Implicit Runge–Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation

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Publication year: 2018

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Authors: Nizam G. Ghawadri, Norazak Senu, Firas A. Fawzi, Fudziah Ismail, Zarina Bibi İbrahim

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Landing page: https://doi.org/10.3390/a12010010

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Concepts: Runge–Kutta methods, Mathematics, Ordinary differential equation, Diagonal, Ode, Numerical methods for ordinary differential equations, L-stability, Type (biology), Explicit and implicit methods, Mathematical analysis, Set (abstract data type), Applied mathematics, Differential equation, Function (biology), Differential algebraic equation, Geometry, Computer science, Ecology, Biology, Evolutionary biology, Programming language

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Cited by: 15

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