Approximate solution of MRLW equation in B-spline environment

Decatic B‐spline collocation scheme for approximate solution of Burgers' equation

“…Several approaches are applied for computing the solution of different partial differential equations such as exponential cubic B‐spline scheme [12] and extended cubic B‐spline with finite element technique [21] for solving numerical solution generalized Burgers' Fisher equation, extended cubic B‐spline for Kdv‐Burgers' equation [22], quartic B‐spline scheme for solving MRLW equation [25, 52], MacCormack/Lax–Friedrichs approach to solve shock‐capturing [3], optimized composite approaches for solving hyperbolic conservative laws [2], Legendre spectral element scheme for generalized Benjamin–Bona–Mahony–Burgers equation [17], and so on [52].…”

Numerical treatment of Kuramoto-Sivashinsky equation on B-spline collocation

“…The present work is related with the construction and implementation of a numerical technique to obtain the approximate solution of Kuramoto-Sivanshinsky equation (KSE) with initial-boundary conditions. The KSE is a great fundamental interest in the same way just as it is famous counterp-arts Korteweg-de Vries-Burger-Kuromato equation (Alimirzaluo & Nadjafikhah, 2019), fractional optical solitons of the space-time fractional nonlinear Schr€ odinger equations (Wu, Yu, & Wang, 2020), nonlinear wave-like equations stated by Kumar, Singh, Purohit, and Swroop (2019), symmetry breaking of infinite-dimensional dynamic system (Hu, Wang, Zhao, & Deng, 2020), vibration and elastic wave propagation in spatial flexible damping panel attached to four special spring (Hu, Zhang, & Deng, 2020), internal resonance of a flexible beam in a spatial tethered system (Hu, Ye, & Deng, 2020), minimum control energy of spatial beam with assumed attitude adjustment target (Hu, Yu, & Deng, 2020), symplectic analysis on orbit-attitude coupling dynamic problem of spatial rigid rod (Hu, Yin, Zheng, & Deng, 2020), interaction effects of DNA, RNA-polymerase, and cellular fluid on the local dynamic behaviours of DNA , different order of ordinary differential equations (Gebremedhin & Jena, 2019, 2020Jena, Mohanty, & Mishra, 2018;Mohanty, Jena, & Mishra, 2020;, B-spline collocation (Jena & Gebremedhin, 2021;Jena, Senapati, & Gebremedhin, 2020a, 2020b) symmetry analysis and rogue wave solutions for the (2 þ 1)dimensional nonlinear Schr€ odinger equation with variable coefficients (Wang, 2016), novel (3 þ 1)dimensional sine-Gorden and sinh-Gorden equation: Derivation symmetries and conservation laws (Wang, 2021), (2 þ 1)-dimensional KdV equation and mKdV equation: symmetries, group invariant solutions and conservation laws (Wang & Kara, 2019), symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics (Wang, Liu, Wu, & Su, 2020), (2 þ 1)-dimensional Boiti-Leon-Pempinelli equation-Domail walls, invariance properties and conservation laws (Wang, Vega-Guzman, Biswas, Kamis Alzahrani, & Kara, 2020), (2 þ 1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solution (Wang, Yang, Gu, Gua...…”

Mathematical Modelling in Engineering with Integral Transforms via Modified Adomian Decomposition Method

“…Three integral transforms Elzaki, Abboodh and Mohand are discussed in the present work to solve linear initial value problems (IVPs) and boundary value problems (BVPs). These techniques are useful for both homogeneous and non-homogeneous linear differential equations which results in exact analytical solution but to obtain approximate solution and to solve nonlinear differential equations intervention of some other methods like Adomian decomposition method [9,10], Differential transformation method [11][12][13][14][15][16][17][18], FDTD Method [19], ARA transform [20], New transform iterative method [21], Coupling Elzaki transform and Homotopy perturbation method [22], Polynomial integral transform [23], modified Adomian decomposition method [24], numerical quadrature for real and analytic functions , B-spline collocation [48][49][50][51] and its subsequent modification rules are essential. Our work comprises the analytic and approximate solution of higherorder IVPs in electrical circuits, mass-spring system, and beam theory.…”