Implicit Methods for Numerical Solution of Singular Initial Value Problems
Habibur Rahaman, M. Kamrul Hasan, Ayub Ali, Md. Shamsul Alam
Abstract
Abstract Various order of implicit method has been formulated for solving initial value problems having an initial singular point. The method provides better result than those obtained by used implicit formulae developed based on Euler and Runge-Kutta methods. Romberg scheme has been used for obtaining more accurate result.
Topics & Concepts
Runge–Kutta methodsEuler's formulaSingular solutionInitial value problemApplied mathematicsMathematicsEuler methodBackward Euler methodScheme (mathematics)Value (mathematics)Point (geometry)Explicit and implicit methodsComputer scienceCalculus (dental)Euler equationsMathematical analysisNumerical analysisDifferential equationOrdinary differential equationGeometryExact differential equationDentistryMedicineStatisticsFractional Differential Equations SolutionsNumerical methods for differential equationsDifferential Equations and Numerical Methods