Results 1 to 10 of about 3,909 (206)
The Solution of Integral Equations in Chebyshev Series [PDF]
Mathematics of Computation, 1969 If the solution of an integral equation can be expanded in the form of a Chebyshev series, the equation can be transformed into an infinite set of algebraic equations in which the unknowns are the coefficients of the Chebyshev series. The algebraic equations are solved by standard iterative procedures, in which it is not necessary to determine ...
R. E. Scraton
openalex +3 more sources
Euler-Chebyshev methods for integro-differential equations [PDF]
Applied Numerical Mathematics, 1997 Some explicit methods are constructed and analysed for solving initial value problems for systems of integro-differential equations with expensive right hand side functions whose Jacobian has its stiff eigenvalues along the negative axis.
P.J. van der Houwen, B.P. Sommeijer
openalex +6 more sources
Computing the strict Chebyshev solution of overdetermined linear equations [PDF]
Mathematics of Computation, 1977 A method for calculating the strict Chebyshev solution of overdetermined systems of linear equations using linear programming techniques is described. This method provides: (1) a way to determine, for the majority of cases, all the equations belonging to the characteristic set, (2) an efficient method to obtain the inverse of the matrix needed to ...
Nabih N. Abdelmalek
+5 more sources
On linear homogeneous differential equation of Chebyshev type
Lietuvos matematikos rinkinys, 2008 Let L[y] = y(n)(z)+gn-1(z)y(n-1)(z)+. . .+g1(z)y(1)(z)+g0(z)y(z) = 0 be a differential equation of nth order with analytic in circle |z| < R coefficients. We will call above equation by equation of Chebyshev type in |z| < R, if fundamental system of its solution is a Chebyshev system in circle |z| < R .
E. G. Kiriyatzkii
openalex +4 more sources
Conformable Fractional Chebyshev Equations and Fractional Chebyshev Polynomials [PDF]
Afyon Kocatepe University Journal of Sciences and Engineering, 2016 Emrah Ünal, Ahmet Gökdoğan
openalex +2 more sources
The Chebyshev Difference Equation [PDF]
Mathematics, 2020 We define and investigate a new class of difference equations related to the classical Chebyshev differential equations of the first and second kind. The resulting “discrete Chebyshev polynomials” of the first and second kind have qualitatively similar properties to their continuous counterparts, including a representation by hypergeometric series ...
Tom Cuchta +2 more
openaire +2 more sources
Chebyshev polynomials in the numerical solution of differential equations [PDF]
Mathematics of Computation, 1977 Amongst satisfactory techniques for the numerical solution of differential equations, the use of Chebyshev series is often avoided because of the tedious nature of the calculations. A systematic application of the Chebyshev method is given for certain fourth order boundary value problems in which the derivatives have polynomial coefficients.
A. G. Morris, T. S. Horner
openaire +3 more sources
Chebyshev expansions for solutions of linear differential equations [PDF]
Proceedings of the 2009 international symposium on Symbolic and algebraic computation, 2009 A Chebyshev expansion is a series in the basis of Chebyshev polynomials of the first kind. When such a series solves a linear differential equation, its coefficients satisfy a linear recurrence equation. We interpret this equation as the numerator of a fraction of linear recurrence operators.
Benoit, Alexandre, Salvy, Bruno
openaire +5 more sources
Friedmann's equations in all dimensions and Chebyshev's theorem [PDF]
Journal of Cosmology and Astroparticle Physics, 2014 Extended and re-organized version to appear in ...
Yisong Yang +4 more
openaire +3 more sources
On a Class of Differential Equations That Contains the Equations of Euler and Chebyshev
Advances in Applied Mathematics, 1997 A general algebraic method, based on generating functions on a class of linear differential equations with variable coefficients that contains the Euler and Chebyshev equations, is treated. This method gives a possibility to find explicit solutions of such equations with given initial conditions.
David Elizarraraz, Luis Verde-Star
openaire +3 more sources