L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems
-
Sania Qureshi
and
Higinio Ramos
Abstract
In this work, we develop a nonlinear explicit method suitable for both autonomous and non-autonomous type of initial value problems in Ordinary Differential Equations (ODEs). The method is found to be third order accurate having L-stability. It is shown that if a variable step-size strategy is employed then the performance of the proposed method is further improved in comparison with other methods of same nature and order. The method is shown to be working well for initial value problems having singular solutions, singularly perturbed and stiff problems, and blow-up ODE problems, which is illustrated using a few numerical experiments.
Acknowledgements:
The authors are grateful to two referees for their careful reading of the manuscript, which helped to improve the final result.
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Articles in the same Issue
- Frontmatter
- Numerical Treatment of the Modified Burgers’ Equation via Backward Differentiation Formulas of Orders Two and Three
- Return Mapping Algorithms (RMAs) for Two-Yield Surface Thermoviscoplastic Models Using the Consistent Tangent Operator
- Synchronization of Multiple Mechanical Oscillators Under Noisy Measurements Signals and Mismatch Parameters
- Nonlinear Wave Modulation in Nanorods Using Nonlocal Elasticity Theory
- Asymptotic Behavior of the Fractional Order three Species Prey–Predator Model
- Continuous Dependence on Data for Solutions of Fractional Extended Fisher–Kolmogorov Equation
- L-stable Explicit Nonlinear Method with Constant and Variable Step-size Formulation for Solving Initial Value Problems
- Weakness and Mittag–Leffler Stability of Solutions for Time-Fractional Keller–Segel Models
- Stability Analysis of Multi-point Boundary Value Problem for Sequential Fractional Differential Equations with Non-instantaneous Impulses
- Existence and Uniqueness of Classical and Mild Solutions of Generalized Impulsive Evolution Equation
- A Collocation Method Based on Jacobi and Fractional Order Jacobi Basis Functions for Multi-Dimensional Distributed-Order Diffusion Equations
- Two-Dimensional Legendre Wavelets for Solving Variable-Order Fractional Nonlinear Advection-Diffusion Equation with Variable Coefficients
