A remark on the parametrization of the numerical solution of boundary value problems

Krasnikov, S. D.; Kuznetsov, E. B.

doi:10.1134/s0012266107070105

Cited by 2 publications

(1 citation statement)

References 2 publications

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“…Преимущества применения дискретного продолжения по параметру отражены в ряде работ, исследующих решение краевых задач для систем дифференциальноалгебраических [5] и обыкновенных дифференциальных [6] уравнений без запаздывания. Использование непрерывного и дискретного методов продолжения по параметру для решения начальных задач для системы интегродифференциально-алгебраических с запаздыванием рассмотрено в [7].…”

Section: Introductionunclassified

The discrete continuation in the boundary value problem for systems of nonlinear differential equations with deviation argument

Afanaseva

Kuznetsov

2019

Zhurnal SVMO

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The solution of the boundary value problems for system of nonlinear differential equations with argument delay is considered in the article. The solution is based on the shooting method. Within its framework the method of continuation with respect to parameter in the Lahaye form, method of the best parametrization and the Newton method are implemented that allow to find possible solutions. To solve the Cauchy problem at each step of the shooting method the discrete continuation method with respect to the best parameter combined with the Newton method is applied. This approach allows to build the solution in the case when singular limit points exist. That provides continuation of Newton iteration process. The algorithm is completed by calculating the Lagrange polynomial to obtain the values of function in the delay points. The example given in the article represents the advantages of the proposed method.

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Section: Introductionunclassified

The discrete continuation in the boundary value problem for systems of nonlinear differential equations with deviation argument

Afanaseva

Kuznetsov

2019

Zhurnal SVMO

View full text Add to dashboard Cite

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Numerical continuation of solution at a singular point of high codimension for systems of nonlinear algebraic or transcendental equations

Krasnikov

Kuznetsov

2016

Comput. Math. and Math. Phys.

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A remark on the parametrization of the numerical solution of boundary value problems

Cited by 2 publications

References 2 publications

The discrete continuation in the boundary value problem for systems of nonlinear differential equations with deviation argument

The discrete continuation in the boundary value problem for systems of nonlinear differential equations with deviation argument

Numerical continuation of solution at a singular point of high codimension for systems of nonlinear algebraic or transcendental equations

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