Fractal non-polynomial spline method for the solution of fourth-order boundary value problems in plate deflection theory

被引：0
作者：
Khatoon, Zainav [1 ]
Sultana, Talat [2 ]
Khan, Arshad [1 ]
机构：
[1] Jamia Millia Islamia, Dept Math, New Delhi 110025, India
[2] Univ Delhi, Dept Math, Lakshmibai Coll, New Delhi 110052, India
来源：
MATHEMATICAL SCIENCES | 2022年 / 16卷 / 04期
关键词：
Fractal non-polynomial spline; Difference equations; Truncation error; Convergence analysis; NUMERICAL-SOLUTION; SYSTEM;
D O I：
10.1007/s40096-021-00429-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A new technique using fractal non-polynomial spline is formulated for approximating the solution of certain fourth-order two-point boundary value problems arising in plate deflection theory. Numerical techniques of second, fourth and almost sixth order are derived which provide five-diagonal linear systems. Convergence analysis of sixth-order method is discussed. Numerical examples are presented to prove the supremacy of developed technique over fractal quintic spline and some other spline techniques.
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收藏
页码：401 / 416
页数：16
相关论文
共 29 条
[11]   NUMERICAL-SOLUTION OF A 4TH-ORDER ORDINARY DIFFERENTIAL-EQUATION [J].
JAIN, MK ;
IYENGAR, SRK ;
SALDANHA, JSV .
JOURNAL OF ENGINEERING MATHEMATICS, 1977, 11 (04) :373-380
[12]   EXPONENTIAL SPLINE APPROACH FOR THE SOLUTION OF NONLINEAR FOURTH-ORDER BOUNDARY VALUE PROBLEMS [J].
Khandelwal, Pooja ;
Khan, Arshad .
PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2018, 104 (118) :265-279
[13]   Numerical solution of fourth-order problems with separated boundary conditions [J].
Loghmani, G. B. ;
Alavizadeh, S. R. .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 191 (02) :571-581
[14]   High order accuracy nonpolynomial spline solutions for 2μth order two point boundary value problems [J].
Ramadan, M. A. ;
Lashien, I. F. ;
Zahra, W. K. .
APPLIED MATHEMATICS AND COMPUTATION, 2008, 204 (02) :920-927
[15]   Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem [J].
Ramadan, M. A. ;
Lashien, I. F. ;
Zahra, W. K. .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (04) :1105-1114
[16]   Non-polynomial spline for solution of boundary-value problems in plate deflection theory [J].
Rashidinia, J. ;
Jalilian, R. .
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2007, 84 (10) :1483-1494
[17]   Non-polynomial spline methods for the solution of a system of obstacle problems [J].
Rashidinia, J. ;
Jalilian, R. ;
Mohammadi, R. .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 188 (02) :1984-1990
[18]   Comment on the paper "A class of methods based on non-polynomial spline functions for the solution of a special fourth-order boundary-value problems with engineering applications" [J].
Rashidinia, J. ;
Jalilian, R. ;
Mohammadi, R. .
APPLIED MATHEMATICS AND COMPUTATION, 2007, 186 (02) :1572-1580
[19]   Convergence of numerical solution of a fourth-order boundary value problem [J].
Rashidinia, J ;
Golbabaee, A .
APPLIED MATHEMATICS AND COMPUTATION, 2005, 171 (02) :1296-1305
[20]  
Rashidinia J, 2009, SCI IRAN TRANS D, V16, P128
123