Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

Noor‐ul‐Amin, Muhammad; Abbas, Muhammad; Iqbal, Muhammad Kashif; Băleanu, Dumitru

doi:10.3389/fphy.2020.00288

Cited by 27 publications

(2 citation statements)

References 50 publications

(63 reference statements)

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“…6th-and 8th-order linear & non-linear BVPs are examined in [18][19][20] and 10th order nonlinear BVPs are disclosed in [21] utilizing CB Spline. A collocation approach based on redefined cubic B-spline (RCBS) functions and finite difference formulation is presented in [22,23] and [24] to study the approximate solution of time fractional Allen-Cahn equation (ACE), time fractional advection diffusion equation and time-fractional Klein-Gordon equation. In [25], authors have explored the numerical solution of fourth-order fractional boundary value problems involving product terms by means of the quintic spline collocation method.…”

Section: Introductionmentioning

confidence: 99%

Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit

Khalid¹,

Rehan

Nisar

et al. 2021

Phys. Scr.

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This study manages the numeric roots of the 7th-order linear & nonlinear boundary value problems (BVPs) utilizing another CB(Cubic-B) spline strategy. Cubic Spline interpolation is a different type of spline interpolation which is utilized very frequently to escape the problem of Runge's phenomenon. That technique provides an interpolating polynomial which is evener and has lesser error than former interpolating polynomials such as Lagrange polynomial and Newton polynomial. The primary thought is that we have altered the BVPs to deliver another framework arrangement of linear equations. We develop the class of numerical techniques for a particular selection of the factors that are associated with CB Spline. The end conditions associated with the BVPs are determined. For each problem, the results obtained by CB Spline is compared with the exact solution. The absolute error(AE) for every iteration is calculated. To show the higher level of preciseness of CB Spline, the absolute errors of the CB Spline has been compared with different techniques such as Modified Decomposition Method(MDM), Differential Transform Method(DTM), Homotopy Perturbation Method(HPM), Variational Iteration technique(VIT) and observed to be more accurate. Graphs that describe the graphical comparison of CB Spline at n=5 and n=10 are also included in this paper. The calculation created here isn't just for the numeric roots of the 7th-order BVPs. It also evaluates the derivative to the 7th-order derivative of the specific solution. A few models are represented, which depicting the practicality and capability of the suggested conspire. Abbreviations CB Spline Cubic B Spline BVPs boundary value problems MDM Modified Decomposition Method DTM Differential Transform Method HPM Homotopy Perturbation Method VIT Variational Iteration technique MAE maximum absolute error RECEIVED

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Section: Introductionmentioning

confidence: 99%

Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit

Khalid¹,

Rehan

Nisar

et al. 2021

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. Applications of spline function in fractional partial differential equations can be found in [5][6][7][8][9][10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

Taghipour

Aminikhah

2021

Mathematical Problems in Engineering

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In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method.

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On the initial value problem for the nonlinear fractional Rayleigh-Stokes equation

Luc

Lân

O’Regan

et al. 2021

J. Fixed Point Theory Appl.

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Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

Cited by 27 publications

References 50 publications

Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit

Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit

A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

On the initial value problem for the nonlinear fractional Rayleigh-Stokes equation

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