A5100655559- Differential Equations and Numerical Methods
- Numerical methods for differential equations
- Nonlinear Waves and Solitons
- Fractional Differential Equations Solutions
- Advanced Numerical Methods in Computational Mathematics
- Computational Fluid Dynamics and Aerodynamics
- Fluid Dynamics and Turbulent Flows
- Simulation Techniques and Applications
Netaji Subhas University of Technology
2023-2024
University of Delhi
2015-2020
Abstract This article focuses on finding numerical solutions of high accuracy and low computational cost for second order Lane-Emden-Fowler type equations. The significance these nonlinear equations is rooted in their ability to model important physical, astrophysical, biological phenomena. proposed study uses cubic spline approximations discretization along with half-step grid points develop a fourth implicit method capable solving highly non-linear singular accuracy. A comprehensive...
In this paper, we present a new numerical method for effectively solving general second-order ordinary differential equations with mixed boundary conditions. Our approach utilizes quasi-variable mesh enabling us the flexibility to adapt density according different layer problems. By employing discretization technique that incorporates construction of exponential spline, achieve third-order accuracy at internal grid points, while points exhibit fourth-order accuracy. Since is based on...
In this article, we propose a new two-level implicit method of accuracy two in time and three space based on spline compression approximations using off-step points central point quasi-variable mesh for the numerical solution system 1D quasi-linear parabolic partial differential equations. The is derived directly from continuity condition first-order derivative function. stability analysis model problem discussed. applicable to problems polar systems. To demonstrate strength utility proposed...
In this article, we discuss a new two-level implicit scheme of order accuracy two in time and four space based on the spline compression approximations for numerical solution 1D unsteady quasi-linear biharmonic equations. We use only half-step points central point uniform mesh derivation method. The proposed method is derived directly from continuity condition first derivative function. For model linear problem, shown to be unconditionally stable. has successfully tested Kuramoto–Sivashinsky...
Abstract In this research, we introduce a two-tier non-polynomial spline approach with graded mesh discretization for addressing fourth-order time-dependent partial differential equations, which find applications in various physical scenarios like the nonlinear Kuramoto-Sivashinsky equation and extended Fisher-Kolmogorov equation. Our method involves considering three spatial points at each time step scheme development, achieving accuracy of temporal two. Notably, our offers advantage...
The present work aims to introduce a novel numerical method for solving second-order two-point mixed boundary value problems. Mixed problems occur in various scientific fields, including quantum mechanics, fluid dynamics, and chemical reactor theory. proposed provides highly accurate, fourth-order convergent solution, achieved by implementing compact finite difference based on non-polynomial spline tension approximations. Notably, the discretisation involves use of half-step grid points,...
<title>Abstract</title> In this article, we present a new numerical method for effectively solving general second-order ordinary differential equations with mixed boundary conditions. Our approach utilizes quasi-variable mesh enabling us the flexibility to adapt density according different layer problems. By employing discretization technique that incorporates construction of exponential spline, achieve third-order accuracy at internal grid points, while points exhibit fourth-order accuracy....