Combining the Shooting Method with an Operational Matrix Method to Solve Two Point Boundary Value Problems

Sahu, Kshama Sagar; Jena, Mahendra Kumar

doi:10.1007/s40819-021-00967-x

Cited by 4 publications

(1 citation statement)

References 26 publications

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“…Furthermore, [10] applied operational matrix method to shooting technique to solve the resulting initial value problems. The hitch of the method under discussion for nonlinear differential equations is how to update the shooting angle or its slope of which the popular methods are Secant and Newton methods.…”

Section: Introductionmentioning

confidence: 99%

New Formulas for Adjusting Shooting Angle in Application of Shooting Method to Boundary Value Problems

Oderinu¹,

Owolabi²,

Alao³

2023

Int. J. of Appl. Math.

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Two new formulas for adjusting shooting angle in the technique of shooting method were formulated. These formulas are modified Newton's formula and a Cubic Newton's formula which were obtained to form Taylor series. The effectiveness of these formulas were investigated by solving two different nonlinear boundary value problems, the results obtained were compared with the regular Newton's formula and both the new methods performed better that the Newton's method with the Cubic having the best performance. This inference is evident from the table of errors, tolerance value which is the absolute difference between two successive iterations also gave credence to the performance of the two formulas.

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Section: Introductionmentioning

confidence: 99%

New Formulas for Adjusting Shooting Angle in Application of Shooting Method to Boundary Value Problems

Oderinu¹,

Owolabi²,

Alao³

2023

Int. J. of Appl. Math.

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Multi-Tree Guided Efficient Robot Motion Planning

Sun

Wang

Meng

2022

Procedia Computer Science

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Shooting-projection method for a small object moving under the influence of a force

Filipov

Faragó

Avdzhieva

2021

J. Phys.: Conf. Ser.

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We consider a small object in 3D moving under the influence of a force that may depend explicitly on time, on the position of the object, and on its velocity. The equations of motion of classical mechanics are assumed to hold. If the position of the object is specified at some initial and some final time, obtaining the trajectory of the object requires the solution of a two-point boundary value problem. To solve the problem various numerical technics can be applied. This paper extends the recently proposed shooting-projection method to 3D. We introduce a Lagrangian from which, applying the principle of least action, the projection trajectory is derived. Analysis of the action reveals the meaning of the projection trajectory. Using the shooting-projection method, the considered two-point boundary value problem is solved for the case of a projectile motion in the presence of air resistance and wind.

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Combining the Shooting Method with an Operational Matrix Method to Solve Two Point Boundary Value Problems

Cited by 4 publications

References 26 publications

New Formulas for Adjusting Shooting Angle in Application of Shooting Method to Boundary Value Problems

New Formulas for Adjusting Shooting Angle in Application of Shooting Method to Boundary Value Problems

Multi-Tree Guided Efficient Robot Motion Planning

Shooting-projection method for a small object moving under the influence of a force

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