Summary
In thispaper we formulate and prove the basic principles of a procedure for computing a bound on the error in the numerical solution of a system of linear differential equations. The bound on the error at each integration step is expressed in terms of an ellipsoid whose size and orientation is determined by the computations. To illustrate the procedure, Bessel's equation (of order zero) is integrated over the interval 2≦x≦3 at steps of length 0.1 and bounds on the error are given for each step.
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References
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Guderley, K.G., Keller, C.L. A basic theorem in the computation of ellipsoidal error bounds. Numer. Math. 19, 218–229 (1972). https://doi.org/10.1007/BF01404692
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DOI: https://doi.org/10.1007/BF01404692