What are the different numerical methods for solving second-order ODEs?
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Different numerical methods for solving second-order ODEs include the spectral collocation method , the operational matrix method , Newton's interpolation method, and Aitken's method . The spectral collocation method represents the solution as an expansion in Chebyshev polynomials and allows for stable calculation of both the spectral and pointwise representations of the solution. The operational matrix method involves deriving operational matrices for the differential and integral terms of the equation and combining them to generate a single algebraic system. Newton's interpolation and Aitken's methods are used to find exact and analytic results for nonlinear ordinary differential equations. These methods provide efficient and accurate solutions for second-order ODEs .
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23 May 2022 1 Citations | The paper does not mention the specific numerical methods for solving second-order ODEs. |
| The paper discusses the use of Newton's interpolation and Aitken's methods for solving second-order ordinary differential equations. | |
25 Oct 2022 | The paper presents a new method for solving second-order linear differential equations by transforming them into Riccati ordinary differential equations. |
| The paper discusses the use of the operational matrix method for solving second-order two-dimensional symmetric sequential fractional integro-differential equations. |
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