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The Computer Journal 1963 6(1):88-92; doi:10.1093/comjnl/6.1.88
© 1963 by British Computer Society
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The solution of nonlinear ordinary differential equations in Chebyshev series

C. W. Clenshaw and H. J. Norton

Mathematics Dept, N.P.L., Teddington, UK

The paper describes a simple iterative method for obtaining the solution of an ordinary differential equation in the form of a Chebyshev series. Nonlinear terms which occur in the equation are dealt with by evaluating their components at the Chebyshev points (cos r{pi}/N), performing the nonlinear equations and then deriving the representative Chebyshev series for the nonlinear term from its values at the Chebyshev points.


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