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Original Articles

On the application of spline functions to initial value problems with retarded argument

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Pages 173-179 | Received 19 Sep 1988, Published online: 19 Mar 2007

Keep up to date with the latest research on this topic with citation updates for this article.

Read on this site (9)

Mehmet Sezer, Salih Yalçinbaş & Mustafa Gülsu. (2008) A Taylor polynomial approach for solving generalized pantograph equations with nonhomogenous term. International Journal of Computer Mathematics 85:7, pages 1055-1063.
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M. A. El-Khatib. (2003) Convergence of the spline function for functional-differential equation of neutral type . International Journal of Computer Mathematics 80:11, pages 1437-1447.
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A. El-Safty, M. S. Salim & M. A. El-Khatib. (2003) Convergence Of The Spline Function For Delay Dynamic System. International Journal of Computer Mathematics 80:4, pages 509-518.
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M.S. Salim. (2002) Existence, Uniqueness and Applications of the Spline Method for Functional-Differential Equation of Neutral Type. International Journal of Computer Mathematics 79:6, pages 775-788.
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A. El-Safty, M.S. Salim & M.A. El-Khatib. (2001) Existence, uniqueness and stability of the spline function for delay controlled dynamic system. International Journal of Computer Mathematics 77:4, pages 629-640.
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A. El-Safty & Shadia M. Abo-Hasha. (2000) Stability of 2h-step spline method for delay differential equations. International Journal of Computer Mathematics 74:3, pages 315-324.
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P. Blaga, G. Micula & M. Micula. (1997) The numerical solution of differential equations with retarded argument by means of natural spline functions of even degree. International Journal of Computer Mathematics 64:3-4, pages 245-262.
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M. A. -K. Ibrahim, A. El-Safty & Shadia M. Abo-Hasha. (1996) Application of spline functions to neutral delay-differential equations. International Journal of Computer Mathematics 62:3-4, pages 233-239.
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M. A. -K. Ibrahim, A. El-Safty & Shadia M. Abo-Hasha. (1994) On the p-stability of quadratic spline for delay differential equations. International Journal of Computer Mathematics 52:3-4, pages 219-223.
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Articles from other publishers (13)

Mohammad Abu-Ghuwaleh, Rania Saadeh & Rasheed Saffaf. (2024) Master generators: A novel approach to construct and solve ordinary differential equations. Mathematics and Computers in Simulation 218, pages 600-623.
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Hamood. M. Yousef & A. I. B. MD. Ismail. Application of the Laplace Adomian decomposition method for solution system of delay differential equations with initial value problem. Application of the Laplace Adomian decomposition method for solution system of delay differential equations with initial value problem.
Eid H. Doha, Ali H. Bhrawy & Ramy M. Hafez. (2017) Numerical algorithm for solving multi-pantograph delay equations on the half-line using Jacobi rational functions with convergence analysis. Acta Mathematicae Applicatae Sinica, English Series 33:2, pages 297-310.
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E. H. Doha, D. Baleanu, A. H. Bhrawy & R. M. Hafez. (2014) A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions. Abstract and Applied Analysis 2014, pages 1-9.
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Tuğçe Akkaya, Salih Yalçinbaş & Mehmet Sezer. (2013) Numeric solutions for the pantograph type delay differential equation using First Boubaker polynomials. Applied Mathematics and Computation 219:17, pages 9484-9492.
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Sabir Widatalla. (2012) A Comparative Study on the Stability of Laplace-Adomian Algorithm and Numerical Methods in Generalized Pantograph Equations. ISRN Computational Mathematics 2012, pages 1-6.
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Mustafa Gülsu & Mehmet Sezer. (2011) A taylor collocation method for solving high-order linear pantograph equations with linear functional argument. Numerical Methods for Partial Differential Equations 27:6, pages 1628-1638.
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Mustafa Gülsu, Burcu Gürbüz, Yalçın Öztürk & Mehmet Sezer. (2011) Laguerre polynomial approach for solving linear delay difference equations. Applied Mathematics and Computation 217:15, pages 6765-6776.
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Mustafa Gülsu & Mehmet Sezer. (2011) A collocation approach for the numerical solution of certain linear retarded and advanced integrodifferential equations with linear functional arguments. Numerical Methods for Partial Differential Equations 27:2, pages 447-459.
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O.A. Taiwo & O.S. Odetunde. (2010) On the Numerical Approximation of Delay Differential Equations by a Decomposition Method. Asian Journal of Mathematics & Statistics 3:4, pages 237-243.
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Mehmet Sezer & Ayşegül Akyüz-Daşcıogˇlu. (2007) A Taylor method for numerical solution of generalized pantograph equations with linear functional argument. Journal of Computational and Applied Mathematics 200:1, pages 217-225.
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Gheorghe Micula & Sanda MiculaGheorghe Micula & Sanda Micula. 1999. Handbook of Splines. Handbook of Splines 383 600 .
M.A.-K. Ibrahim, A. El-Safty & S.M. Abo-Hasha. (1995) 2h-Step spline method for the solution of delay differential equations. Computers & Mathematics with Applications 29:8, pages 1-6.
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