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International Journal of Computer Mathematics Volume 70, 1999 - Issue 3
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Original Articles

Generalized trapezoidal formulas for parabolic equations

M.M. Chawla Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait
,
M.A Al-Zanaidi Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat, 13060, Kuwait
&
D.J Evans Faculty of Engineering and Computing, Nottingham Trent University, Burton Street, Nottingham, NG1 4BU, UK
Pages 429-443 | Received 11 Apr 1998, Published online: 19 Mar 2007

Citations (28)

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Read on this site (9)

M. M. Chawla & D. J. Evans. (2005) A new L-stable Simpson-type rule for the diffusion equation. International Journal of Computer Mathematics 82:5, pages 601-607.
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S. Sallam, M. Naim Anwar & M. R. Abdel-Aziz. (2004) Unconditionally stable C1-cubic spline collocation method for solving parabolic equations. International Journal of Computer Mathematics 81:7, pages 813-821.
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M. M. Chawla, M. A. Al-Zanaidi & D. J. Evans. (2004) Generalized trapezoidal formulas for valuing American options . International Journal of Computer Mathematics 81:3, pages 375-381.
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M. M. Chawla, M. A. Al-Zanaidi & D. J. Evans. (2003) Generalized trapezoidal formulas for the black–scholes equation of option pricing . International Journal of Computer Mathematics 80:12, pages 1521-1526.
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M. M. Chawla, M. A. Al-Zanaidi & D. J. Evans. (2002) Generalized Trapezoidal Formulas For The Symmetric Heat Equation In Polar Coordinates II. The Case Of Point Sources. International Journal of Computer Mathematics 79:11, pages 1187-1200.
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M.M. Chawla, M.A. Al-Zanaidi & D.J. Evans. (2002) Generalized Trapezoidal Formulas for the Symmetric Heat Equation in Polar Coordinates. International Journal of Computer Mathematics 79:6, pages 729-745.
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M. M. Chawla, M. A. Al-Zanaidi & D. J. Evans. (2001) Lod generalized trapezoidal formula schemes for parabolic differential equations in two space dimensions. International Journal of Computer Mathematics 78:2, pages 269-287.
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M.M. Chawla, M.A. Al-Zanaidi & D.J. Evans. (2001) An alternating direction generalized trapezoidal formula scheme for parabolic differential equations in two space dimensions. International Journal of Computer Mathematics 77:4, pages 611-628.
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M.M. Chawla, M.A. Al-zanaidi & D.J. Evans. (2000) Linearly implicit generalized trapezoidal formulas for nonlinear differential equations. International Journal of Computer Mathematics 74:3, pages 345-359.
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Articles from other publishers (19)

Mukesh Kumar Rawani, Amit Kumar Verma & Lajja Verma. (2024) Numerical treatment of Burgers' equation based on weakly L-stable generalized time integration formula with the NSFD scheme. Applied Mathematics and Computation 467, pages 128485.
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Roushan Kumar, Rakhi Tiwari & Rashmi Prasad. 2023. Mathematics and Computer Science Volume 1. Mathematics and Computer Science Volume 1 353 372 .
Mukesh Kumar Rawani, Lajja Verma, Amit Kumar Verma & Ravi P. Agarwal. (2021) On a weakly L ‐stable time integration formula coupled with nonstandard finite difference scheme with application to nonlinear parabolic partial differential equations . Mathematical Methods in the Applied Sciences 45:3, pages 1276-1298.
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Amit Kumar Verma, Mukesh Kumar Rawani & Ravi P. Agarwal. (2020) A High-Order Weakly L-Stable Time Integration Scheme with an Application to Burgers’ Equation. Computation 8:3, pages 72.
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Gaoyi Wu, Yong Li & Gonglin Yuan. (2018) A Three-Term Conjugate Gradient Algorithm with Quadratic Convergence for Unconstrained Optimization Problems. Mathematical Problems in Engineering 2018, pages 1-15.
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Aijia Ouyang, Li-Bin Liu, Zhou Sheng & Fan Wu. (2015) A Class of Parameter Estimation Methods for Nonlinear Muskingum Model Using Hybrid Invasive Weed Optimization Algorithm. Mathematical Problems in Engineering 2015, pages 1-15.
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Zhou Sheng, Aijia Ouyang, Li-Bin Liu & Gonglin Yuan. (2014) A Novel Parameter Estimation Method for Muskingum Model Using New Newton-Type Trust Region Algorithm. Mathematical Problems in Engineering 2014, pages 1-7.
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Li-Bin Liu & Huan-Wen Liu. (2013) Compact difference schemes for solving telegraphic equations with Neumann boundary conditions. Applied Mathematics and Computation 219:19, pages 10112-10121.
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Lajja Verma. (2012) -Stable Derivative-Free Error-Corrected Trapezoidal Rule for Burgers' Equation with Inconsistent Initial and Boundary Conditions. International Journal of Mathematics and Mathematical Sciences 2012, pages 1-13.
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K. Pandey, Lajja Verma & Amit K. Verma. (2011) L-stable Simpson’s 3/8 rule and Burgers’ equation. Applied Mathematics and Computation 218:4, pages 1342-1352.
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Huai-Huo Cao, Li-Bin Liu & Yong Zhang. (2011) Numerical Solution of Telegraphic Equations with Source Term Using the Generalized Trapezoidal Formula. Numerical Solution of Telegraphic Equations with Source Term Using the Generalized Trapezoidal Formula.
Yong Zhang, Li-Bin Liu & Huai-Huo Cao. (2010) Parametric Cubic Spline Methods for Solving Hyperbolic Equations. Parametric Cubic Spline Methods for Solving Hyperbolic Equations.
Tang-Wei Liu, Li-Bin Liu, He-Hua Xu & Li-Hua Le. (2010) A New Two Level Difference Scheme for Solving One-Dimensional Second-Order Hyperbolic Equations. A New Two Level Difference Scheme for Solving One-Dimensional Second-Order Hyperbolic Equations.
Li-Bin Liu & Huan-Wen Liu. (2010) Quartic spline methods for solving one-dimensional telegraphic equations. Applied Mathematics and Computation 216:3, pages 951-958.
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Hengfei Ding & Yuxin Zhang. (2008) Parameters spline methods for the solution of hyperbolic equations. Applied Mathematics and Computation 204:2, pages 938-941.
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J. Rashidinia, R. Jalilian & V. Kazemi. (2007) Spline methods for the solutions of hyperbolic equations. Applied Mathematics and Computation 190:1, pages 882-886.
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A.A. Salama & H.Z. Zidan. (2006) Fourth-Order Schemes of Exponential Type for Singularly Perturbed Parabolic Partial Differential Equations. Rocky Mountain Journal of Mathematics 36:3.
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Zoltán Horváth. (2005) On the positivity step size threshold of Runge–Kutta methods. Applied Numerical Mathematics 53:2-4, pages 341-356.
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M.M. Chawla, M.A. Al-Zanaidi & M.G. Al-Aslab. (2000) Extended one-step time-integration schemes for convection-diffusion equations. Computers & Mathematics with Applications 39:3-4, pages 71-84.
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