Initial value problems for a system of nonlinear equations on a half-line

AbstractIn this paper, we consider the development and implementation of algorithms for the solution of stiff first order initial value problems. Method of interpolation and collocation of basis function to give system of nonlinear equations which is solved for the unknown parameters to give a continuous scheme that is evaluated at selected grid points to give discrete methods. The stability properties of the method is verified and numerical experiments show that the new method is efficient in handling stiff problems.

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A study on optimally constructed compactly supported orthogonal wavelet filters

Computer Science and Information Systems ◽

10.2298/csis210410052f ◽

2021 ◽

pp. 52-52

Author(s):

Yongkai Fan ◽

Qian Hu ◽

Yun Pan ◽

Chaosheng Huang ◽

Chao Chen ◽

...

Keyword(s):

Nonlinear Equations ◽

System Of Nonlinear Equations ◽

Orthogonal Wavelet ◽

Initial Value ◽

Vanishing Moments ◽

Type Method ◽

Wavelet Filters ◽

Compactly Supported ◽

Elementary Method ◽

Newton Iteration Method

Compactly supported orthogonal wavelet filters are extensively applied to the analysis and description of abrupt signals in fields such as multimedia. Based on the application of an elementary method for compactly supported orthogonal wavelet filters and the construction of a system of nonlinear equations for filter coefficients, we design compactly supported orthogonal wavelet filters, in which both the scaling and wavelet functions have many vanishing moments, by approximately solving the system of nonlinear equations. However, when solving such a system about filter coefficients of compactly supported wavelets, the most widely used method, the Newton Iteration method, cannot converge to the solution if the selected initial value is not near the exact solution. For such, we propose optimization algorithms for the Gauss-Newton type method that expand the selection range of initial values. The proposed method is optimal and promising when compared to other works, by analyzing the experimental results obtained in terms of accuracy, iteration times, solution speed, and complexity.

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Fractional nonlinear systems with sequential operators

Open Physics ◽

10.2478/s11534-013-0223-3 ◽

2013 ◽

Vol 11 (10) ◽

Cited By ~ 7

Author(s):

Dorota Mozyrska ◽

Ewa Girejko ◽

Małgorzata Wyrwas

Keyword(s):

Nonlinear Systems ◽

Nonlinear Equations ◽

Initial Value Problems ◽

Continuous Case ◽

Difference Operators ◽

Initial Value ◽

Numerical Examples ◽

Caputo Derivatives ◽

Derivatives Of

AbstractIn the paper possible approximation of solutions to initial value problems stated for fractional nonlinear equations with sequential derivatives of Caputo type is presented. We proved that values of Caputo derivatives in continuous case can be approximated by corresponding values of h-difference operators with h being small enough. Numerical examples are presented.

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The Double Step Hybrid Linear Multistep Method for Solving Second Order Initial Value Problems

Asian Research Journal of Mathematics ◽

10.9734/arjom/2019/v15i230145 ◽

2019 ◽

pp. 1-11

Author(s):

Y. Skwame ◽

J. Z. Donald ◽

T. Y. Kyagya ◽

J. Sabo

Keyword(s):

Approximate Solution ◽

Initial Value Problems ◽

Multistep Method ◽

Second Order ◽

System Of Nonlinear Equations ◽

Linear Multistep Method ◽

Block Method ◽

Initial Value ◽

Double Step ◽

Grid Points

In this paper, we develop the double step hybrid linear multistep method for solving second order initial value problems via interpolation and collocation method of power series approximate solution to give a system of nonlinear equations which is solved to give a continuous hybrid linear multistep method. The continuous hybrid linear multistep method is solved for the independent solutions to give a continuous hybrid block method which is then evaluated at some selected grid points to give a discrete block method. The basic numerical properties of the hybrid block method was established and found to be zero-stable, consistent and convergent. The efficiency of the new method was conformed on some initial value problems and found to give better approximation than the existing methods.

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Numerical Solution of Fuzzy Initial Value Problems by Fourth Order Runge-Kutta Method Based on Contraharmonic Mean

Indian Journal Of Applied Research ◽

10.15373/2249555x/apr2013/111 ◽

2011 ◽

Vol 3 (4) ◽

pp. 59-63 ◽

Cited By ~ 1

Author(s):

R. Gethsi Sharmila ◽

◽

E. C. Henry Amirtharaj

Keyword(s):

Numerical Solution ◽

Fourth Order ◽

Initial Value Problems ◽

Kutta Method ◽

Initial Value ◽

Runge Kutta Method ◽

Contraharmonic Mean ◽

Runge Kutta

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Mathematical Models of Papermaking

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2001.6.1.15221 ◽

2001 ◽

Vol 6 (1) ◽

pp. 9-19 ◽

Cited By ~ 1

Author(s):

A. Buikis ◽

J. Cepitis ◽

H. Kalis ◽

A. Reinfelds ◽

A. Ancitis ◽

...

Keyword(s):

Mathematical Model ◽

Initial Value Problems ◽

Moisture Transfer ◽

Bound Water ◽

Drying Process ◽

Initial Value ◽

First Order ◽

Heat And Moisture ◽

The Mathematical Model ◽

The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations.

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