scholarly journals Bezier Curves Method for Fourth-Order Integrodifferential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
F. Ghomanjani ◽  
A. V. Kamyad ◽  
A. Kılıçman
Keyword(s):  
Fourth Order ◽  
Necessary Conditions ◽  
Integrodifferential Equations ◽  
Lagrange Equations ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Calculus Of Variation ◽  
Numerical Examples ◽  
Linear And Nonlinear

The Bezier curves method is applied to solve both linear and nonlinear BVPs for fourth-order integrodifferential equations. Also, the presented method is developed for solving BVPs which arise from the problems in calculus of variation. These BVPs result from the Euler-Lagrange equations which are the necessary conditions of the extremums of problems in calculus of variation. Some numerical examples demonstrate the validity and applicability of the technique.

scholarly journals Numerical Solution for IVP in Volterra Type Linear Integrodifferential Equations System

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
F. Ghomanjani ◽  
A. Kılıçman ◽  
S. Effati
Keyword(s):  
Numerical Solution ◽  
Integrodifferential Equations ◽  
Control Points ◽  
Volterra Type ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Numerical Examples ◽  
Piecewise Polynomials

A method is proposed to determine the numerical solution of system of linear Volterra integrodifferential equations (IDEs) by using Bezier curves. The Bezier curves are chosen as piecewise polynomials of degreen, and Bezier curves are determined on[t0, tf ]by n+1control points. The efficiency and applicability of the presented method are illustrated by some numerical examples.

scholarly journals Bernstein Polynomials

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Anandaram Mandyam N
Keyword(s):  
Fourth Order ◽  
Bernstein Polynomials ◽  
Basis Functions ◽  
Spline Functions ◽  
Bezier Curves ◽  
Bézier Curves ◽  
B Splines

Bernstein polynomials (aka, B-polys) have excellent properties allowing them to be used as basis functions in many applications of physics. In this paper, a brief tutorial description of their properties is given and then their use in obtaining B-polys, B-splines or Basis spline functions, Bezier curves and ODE solution curves, is computationally demonstrated.  An example is also described showing their application to solving a fourth-order BVP relating to the bending at the free end of a cantilever.

scholarly journals Modelling of joining route segments of different curvature

2016 ◽  
Vol 11 (1) ◽  
pp. 1-10
Author(s):  
Władysław Koc ◽  
Katarzyna Palikowska
Keyword(s):  
Differential Equations ◽  
Dynamic Model ◽  
Dynamic Properties ◽  
Transition Curve ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Circular Arcs ◽  
Pythagorean Hodograph ◽  
Linear And Nonlinear ◽  
General Method

The paper presents a new general method of modelling route segments curvature using differential equations. The method enables joining of route segments of different curvature. Transitional curves of linear and nonlinear curvatures have been identified in the case of joining two circular arcs by S-shaped and C-oval transitions. The obtained S-shaped curves have been compared to the cubic C-Bezier curves and to the Pythagorean hodograph quantic Bezier curve using the Lateral Change of Acceleration diagram and the dynamic model. The analysis of dynamic properties has showed an advantage of the obtained transition curve of nonlinear curvature over Bezier curves.

scholarly journals Bezier Curves for Solving Fredholm Integral Equations of the Second Kind

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
F. Ghomanjani ◽  
M. H. Farahi ◽  
A. Kılıçman
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Direct Algorithm ◽  
Control Points ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Numerical Examples ◽  
Piecewise Polynomials

The Bezier curves are presented to estimate the solution of the linear Fredholm integral equation of the second kind. A direct algorithm for solving this problem is given. We have chosen the Bezier curves as piecewise polynomials of degreenand determine Bezier curves on [0, 1] byn+1control points. Numerical examples illustrate that the algorithm is applicable and very easy to use.

scholarly journals Quasi-Bézier Curves with Shape Parameters

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Jun Chen
Keyword(s):  
Convex Hull ◽  
Basis Functions ◽  
Geometrical Shape ◽  
Control Points ◽  
Shape Parameters ◽  
Bezier Curves ◽  
Bézier Curves ◽  
Numerical Examples ◽  
Universal Form ◽  
Special Cases

The universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding Quasi-Bézier curves were constructed step-by-step in this paper, using the method of undetermined coefficients. The series of Quasi-Bézier curves had geometric and affine invariability, convex hull property, symmetry, interpolation at the endpoints and tangent edges at the endpoints, and shape adjustability while maintaining the control points. Various existing Quasi-Bézier curves became special cases in the series. The obvious geometric significance of shape parameters made the adjustment of the geometrical shape easier for the designer. The numerical examples indicated that the algorithm was valid and can easily be applied.

scholarly journals A Collocation Method Based on the Bernoulli Operational Matrix for Solving Nonlinear BVPs Which Arise from the Problems in Calculus of Variation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Emran Tohidi ◽  
Adem Kılıçman
Keyword(s):  
Collocation Method ◽  
Necessary Conditions ◽  
Operational Matrix ◽  
Bernoulli Polynomials ◽  
Variational Problems ◽  
Operational Matrices ◽  
Algebraic Equations ◽  
Lagrange Equations ◽  
Calculus Of Variation ◽  
Operational Matrix Of Differentiation

A new collocation method is developed for solving BVPs which arise from the problems in calculus of variation. These BVPs result from the Euler-Lagrange equations, which are the necessary conditions of the extremums of problems in calculus of variation. The proposed method is based upon the Bernoulli polynomials approximation together with their operational matrix of differentiation. After imposing the collocation nodes to the main BVPs, we reduce the variational problems to the solution of algebraic equations. It should be noted that the robustness of operational matrices of differentiation with respect to the integration ones is shown through illustrative examples. Complete comparisons with other methods and superior results confirm the validity and applicability of the presented method.

Quadratic Bezier Curves for Multi-Agent Coordinated Arrival in the Presence of Obstacles

2021 ◽  
Author(s):  
Satyanarayana G. Manyam ◽  
David Casbeer ◽  
Isaac E. Weintraub ◽  
Dzung M. Tran ◽  
Justin M. Bradley ◽  
...  
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Multi Agent

Curves used in highway design and Bezier curves

2021 ◽  
Vol Accepted ◽  
Author(s):  
Bayram Şahin ◽  
Aslı Ayar
Keyword(s):  
Bezier Curves ◽  
Bézier Curves ◽  
Highway Design
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