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Applied Mathematics and Computation, ISSN 0096-3003, 04/2020, Volume 370, p. 124915
•An accurate method is developed for Volterra-Fredholm integral equations.•To design the method, a new shifted piecewise cosine basis functions are... 
Volterra–Fredholm integral equations | Nonlinear equations | Piecewise cosine basis | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | BLOCK-PULSE FUNCTIONS | Volterra-Fredholm integral equations | COMPUTATIONAL METHOD | SOLVE | 2ND KIND | SPREAD
Journal Article
Journal of Chemical Physics, ISSN 0021-9606, 06/2011, Volume 134, Issue 24, pp. 244905 - 244905-14
We provide an in-depth study of pseudo-spectral numerical methods associated with modeling the self-assembly of molten mixed polymer brushes in the framework... 
THIN-FILMS | GRAFTED POLYMERS | mixing | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | convergence of numerical methods | ADSORPTION | HOMOPOLYMER | self-assembly | CONSISTENT-FIELD THEORY | free energy | PARTIAL-DIFFERENTIAL-EQUATIONS | DIBLOCK COPOLYMER | polymer melts | ATTRACTION | STRONG-STRETCHING THEORY | SCF calculations | BLOCK-COPOLYMER
Journal Article
Journal of Process Control, ISSN 0959-1524, 10/2014, Volume 24, Issue 10, pp. 1639 - 1645
•Hybrid spectral methods are proposed for optimal design of fractional order linear SISO system.•Arbitrary stochastic input/parametric uncertainties are... 
Operational matrix | Block pulse function | Polynomial chaos | Stochastic collocation | Fractional calculus | ENGINEERING, CHEMICAL | AUTOMATION & CONTROL SYSTEMS
Journal Article
Numerical Mathematics, ISSN 1004-8979, 05/2013, Volume 6, Issue 2, pp. 424 - 446
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 11/2012, Volume 17, Issue 11, pp. 4262 - 4273
► Numerical scheme for analysis affection of uncertainties in linear SISO fractional order. ► Address both random parameters and stochastic additive input. ►... 
Operational matrix | Block pulse functions | Polynomial chaos | Stochastic collocation | Fractional calculus | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL | Correlation | Monte Carlo methods | Uncertainty | Materials handling | Mathematical models | Matrices | Stochasticity | Spectral methods
Journal Article
Journal of Chemical Physics, ISSN 0021-9606, 06/2014, Volume 140, Issue 22, p. 224101
We present a fast and accurate numerical method for the self-consistent field theory calculations of confined polymer systems. It introduces an exponential... 
DIBLOCK COPOLYMERS | PHASE | MELT | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | COPOLYMER THIN-FILMS | MONTE-CARLO SIMULATIONS | BLOCK-COPOLYMER | Chebyshev approximation | Collocation methods | DIFFUSION EQUATIONS | INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY | SELF-CONSISTENT FIELD | COPOLYMERS | INTERACTIONS | ACCURACY | BOUNDARY CONDITIONS | SURFACES
Journal Article
Mathematical Communications, ISSN 1331-0623, 2014, Volume 19, Issue 2, pp. 417 - 435
In this paper, a new pseudo-spectral (PS) method is developed for solving optimal control problems governed by the non-linear Volterra integral equation (VIE).... 
Hybrid | Block-pulse function | Volterra integral equation | Collocation method | Optimal control | Legendre polynomial | block-pulse function | collocation method | DELAY SYSTEMS | MATHEMATICS | MATHEMATICS, APPLIED | hybrid | BLOCK-PULSE | CHEBYSHEV | EQUATIONS | optimal control
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2020, Volume 43, Issue 1, pp. 384 - 397
Journal Article
Macromolecules, ISSN 0024-9297, 03/2012, Volume 45, Issue 6, pp. 2905 - 2919
An efficient numerical self-consistent field theory (SCFT) algorithm is developed for polymer systems subject to nonperiodic boundary conditions. The method... 
PHASES | POLYMER SCIENCE | MELT | DIBLOCK COPOLYMER | SURFACE | COPOLYMER THIN-FILMS | NONLINEAR SCHRODINGER-EQUATION | MONTE-CARLO SIMULATIONS | BLOCK-COPOLYMER | BLENDS | DROPLETS
Journal Article
Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 11/2011, Volume 27, Issue 6, pp. 1707 - 1721
In this study, a Hermite matrix method is presented to solve high‐order linear Fredholm integro‐differential equations with variable coefficients under the... 
collocation method | Fredholm integro‐differential equations | Hermite series | Hermite polynomials | Fredholm integro-differential equations | MATHEMATICS, APPLIED | TAYLOR POLYNOMIALS | TERMS | TAU-METHOD | INTEGRAL-EQUATIONS | DIFFERENTIAL-EQUATIONS | POLYNOMIAL SOLUTIONS | SERIES EXPANSION METHOD | NUMERICAL-SOLUTION | BLOCK-PULSE FUNCTIONS | 2ND KIND
Journal Article
Afrika Matematika, ISSN 1012-9405, 6/2018, Volume 29, Issue 3, pp. 531 - 555
We consider a new class of modified block Falkner methods for the direct numerical integration of second-order initial value problems having periodic and... 
65L05 | 65L06 | Oscillatory second order initial-value | Mathematics, general | Mathematics Education | Block multistep methods | Mathematics | History of Mathematical Sciences | Applications of Mathematics | Falkner type methods | Collocation formulation | Falkner-type methods
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 1996, Volume 69, Issue 1, pp. 71 - 80
When a Chebyshev spectral collocation method is applied to a flow problem in a rectangularly decomposable domain it leads to the solution of a structured... 
High performance solution | Almost block diagonal systems | Collocation | Domain decomposition | Spectral methods | MATHEMATICS, APPLIED | almost block diagonal systems | collocation | spectral methods | domain decomposition | CRAY Y-MP | ELIMINATION | BLOCK DIAGONAL SYSTEMS | ALGORITHMS | high performance solution | LAMINAR-FLOW | PARALLEL
Journal Article
Linear Algebra and Its Applications, ISSN 0024-3795, 2003, Volume 369, pp. 41 - 75
In the past few years several authors have studied the preconditioning of collocation matrices by finite differences (FDs) matrices arising from the associated... 
Elliptic operators | Collocation methods | Ergodic theorems | Toeplitz matrices | Preconditioning | Finite differences | ergodic theorems | MATHEMATICS, APPLIED | BLOCK TOEPLITZ MATRICES | SEQUENCES | CONVERGENCE | finite differences | collocation methods | OPERATORS | elliptic operators | preconditioning
Journal Article
International Journal of Computer Mathematics, ISSN 0020-7160, 11/2018, Volume 95, Issue 11, pp. 2287 - 2307
Journal Article
12/2014, Volume 19, Issue 2
In this paper, a new pseudo-spectral (PS) method is developed for solving optimal controproblems governed by the non-linear Volterra integral equation(VIE).... 
block-pulse function | collocation method | hybrid | Optimal control | Volterra integral equation | Legendre polynomial
Paper
Numerical Analysis and Applications, ISSN 1995-4239, 7/2017, Volume 10, Issue 3, pp. 272 - 286
Based on the collocation technique, we introduced a unifying approach for deriving a family of multi-point numerical integrators with trigonometric... 
periodic solution | block method | trigonometric coefficients | Numerical Analysis | collocation technique | Mathematics, general | Mathematics | Differential equations
Journal Article
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