High-Order Compact Finite Difference Scheme for Euler–Bernoulli Beam Equation

Pathak, Maheshwar; Joshi, Pratibha

doi:10.1007/978-981-13-0761-4_35

Search citation statements

Order By: Relevance

Paper Sections

Select...

Numerical Examples1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2020

2022

Publication Types

Select...

Article2

Relationship

Self Cite1

Independent1

Authors

Journals

Cited by 2 publications

(2 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is claimed by many iterative methods but when we run higher iterations either the methods start getting very complicated or get stuck. The proposed method is very fast and does not get stuck at higher iterations which is a great advantage of the current method over many iterative methods for the solution of linear [22,23] and nonlinear problems.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Numerical Approximation of Nonlinear Duffing Oscillator Using a Coupled Approach

Joshi¹,

Pathak²

2022

MMEP

Self Cite

View full text Add to dashboard Cite

Duffing equation can describe many important nonlinear physical systems. In this paper a coupled approach based on quasilinearization and Bessel polynomial collocation method has been suggested to solve nonlinear duffing oscillator equation. The nonlinearity in duffing oscillator can be of various variety. This approach is very efficient, stable and reliable to deal with any kind of nonlinearity. Numerical examples demonstrate the validity and applicability of the approach on various types of nonlinear duffing oscillator equation.

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

“…The error also reduces as we run higher iterations. 𝑦"(𝑥) + 𝑘𝑦′ = −𝑦 3 (𝑥) with the initial conditions 𝑦(0) = 𝛼, 𝑦 ′ (0) = 𝛽 (22) Here we have considered the case of α=β=k=1. The linearized form of the Eq.…”

mentioning

confidence: 99%