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International Journal of Computer Mathematics Volume 93, 2016 - Issue 1
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Original Articles

Cubic Hermite collocation solution of Kuramoto–Sivashinsky equation

Ishfaq Ahmad GanaieDepartment of Mathematics, SLIET Longowal, Punjab – 148106, India
,
Shelly AroraDepartment of Mathematics, Punjabi University, Patiala, Punjab – 147002, India
&
V.K. KukrejaDepartment of Mathematics, SLIET Longowal, Punjab – 148106, IndiaCorrespondence[email protected]
Pages 223-235 | Received 08 Jan 2014, Accepted 08 Dec 2014, Published online: 13 Jan 2015

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R. K. Mohanty & Deepti Kaur. (2019) High accuracy two-level implicit compact difference scheme for 1D unsteady biharmonic problem of first kind: application to the generalized Kuramoto–Sivashinsky equation. Journal of Difference Equations and Applications 25:2, pages 243-261.
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Articles from other publishers (15)

R. K. Mohanty & Divya Sharma. (2024) A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto–Sivashinsky and Fisher–Kolmogorov equations. Journal of Mathematical Chemistry 62:5, pages 973-1011.
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Priyanka, Shelly Arora, Fateh Mebrek-Oudina & Saroj Sahani. (2023) Super convergence analysis of fully discrete Hermite splines to simulate wave behaviour of Kuramoto–Sivashinsky equation. Wave Motion 121, pages 103187.
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Archna Kumari & Vijay K. Kukreja. (2023) Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations. Mathematics 11:14, pages 3157.
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Archna Kumari & Vijay Kumar Kukreja. (2023) Study of 4 order Kuramoto-Sivashinsky equation by septic Hermite collocation method. Applied Numerical Mathematics 188, pages 88-105.
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H.R. Marasi & M.H. Derakhshan. (2023) Numerical simulation of time variable fractional order mobile–immobile advection–dispersion model based on an efficient hybrid numerical method with stability and convergence analysis. Mathematics and Computers in Simulation 205, pages 368-389.
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Shelly Arora, Rajiv Jain & V.K. Kukreja. (2022) A robust Hermite spline collocation technique to study generalized Burgers-Huxley equation, generalized Burgers-Fisher equation and Modified Burgers’ equation. Journal of Ocean Engineering and Science.
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Shallu & Vijay Kumar Kukreja. (2021) An improvised extrapolated collocation algorithm for solving Kuramoto–Sivashinsky equation. Mathematical Methods in the Applied Sciences 45:3, pages 1451-1467.
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R. K. Mohanty & Sachin Sharma. (2020) A new high-resolution two-level implicit method based on non-polynomial spline in tension approximations for time-dependent quasi-linear biharmonic equations with engineering applications. Engineering with Computers 37:3, pages 2073-2087.
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R. K. Mohanty & Sachin Sharma. (2019) A new two-level implicit scheme based on cubic spline approximations for the 1D time-dependent quasilinear biharmonic problems. Engineering with Computers 36:4, pages 1485-1498.
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Shelly Arora, Rajiv Jain & V.K. Kukreja. (2020) Solution of Benjamin-Bona-Mahony-Burgers equation using collocation method with quintic Hermite splines. Applied Numerical Mathematics 154, pages 1-16.
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Deepti Kaur & R.K. Mohanty. (2019) Two-level implicit high order method based on half-step discretization for 1D unsteady biharmonic problems of first kind. Applied Numerical Mathematics 139, pages 1-14.
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R. K. Mohanty, Sachin Sharma & Swarn Singh. (2018) A new two-level implicit scheme of order two in time and four in space based on half-step spline in compression approximations for unsteady 1D quasi-linear biharmonic equations. Advances in Difference Equations 2018:1.
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R. K. Mohanty & D. Kaur. (2018) Compact Difference Scheme with High Accuracy for One-Dimensional Unsteady Quasi-Linear Biharmonic Problem of Second Kind: Application to Physical Problems. Numerical Analysis and Applications 11:1, pages 45-59.
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R. K. Mohanty & Deepti Kaur. (2016) Numerov type variable mesh approximations for 1D unsteady quasi-linear biharmonic problem: application to Kuramoto-Sivashinsky equation. Numerical Algorithms 74:2, pages 427-459.
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Shelly Arora & Inderpreet Kaur. (2015) Numerical solution of heat conduction problems using orthogonal collocation on finite elements. Journal of the Nigerian Mathematical Society 34:3, pages 286-302.
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