Direct Solution of General Fourth-Order Ordinary Differential EquationsUsing the Diagonally Implicit Runge-Kutta Method
Keywords:
initial value problem, general fourth-order ODEs, implicit Runge-Kuttatype methodsAbstract
The diagonally implicit Runge-Kutta method (DIRKT), fourth-and fifth-order, is developed in this study
to solve general fourth-order ordinary differential equations (ODEs). DIRKTO5 and DIRKTO4,
respectively, are the names of these methods. Both methods consist of three stages. A collection of test
problems were utilized to support the methodologies. The numerical outcomes demonstrated that the
suggested approaches performed better than the implicit Runge-Kutta (RK) methods in terms of precision
and the quantity of the evaluations of function.
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