High accuracy variable mesh method for nonlinear two-point boundary value problems in divergence form

Jain, Manoj; Sharma, Sachin; Mohanty, R. K.

doi:10.1016/j.amc.2015.10.030

Cited by 7 publications

(4 citation statements)

References 19 publications

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“…Finally, substituting the values of C i , for i = −3, −2, ..., n − 1 in equation ( 7) we obtain the approximated analytical solution of equation (11). The numerical solution can be calculated after obtaining the values of γ by trial and error [20].…”

Section: Solution Of Nonlinear Two-point Bvpsmentioning

confidence: 99%

“…Nonlinear two-point boundary value problems have been solved approximately with shooting, finite difference, variational approach, Adomian decomposition, homotopy perturbation being amongst the more frequently used methods. Details on these methods as well as others can be found in [1,2,3,4,5,6,7,8,9,10,11,12,13].…”

Section: Introductionmentioning

confidence: 99%

“…Table 1 summarize some salient points (obtained from [1,2,3,4,5,6,7,8,9,10,11,12,13]) regarding some approximate methods.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hybrid Cubic B-Spline Method for Solving Non-Linear Two-Point Boundary Value Problems

Heilat¹,

Ismail²

2016

Int. J. of Pure and Appl. Math.

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A method based on hybrid cubic B-spline method (HCBSM) is developed, analyzed and applied to solve second-order non-linear two-point boundary value problems. In this method, a free parameter, γ, plays an important role in producing accurate results. Tests on four examples and a comparison of the results with the results obtained using cubic Bspline, extended cubic B-spline and shooting methods indicated that HCBSM is a feasible and accurate method.

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Section: Solution Of Nonlinear Two-point Bvpsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid Cubic B-Spline Method for Solving Non-Linear Two-Point Boundary Value Problems

Heilat¹,

Ismail²

2016

Int. J. of Pure and Appl. Math.

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show abstract

“…In a similar vein, Mohanty [11] employed a variable mesh discretization technique to effectively solve singular BVPs subject to Dirichlet boundary conditions. Similarly, in their work, Jain et al [12] introduced highly precise variable mesh methods of third order accuracy to address two-point BVPs with Dirichlet boundary conditions. Compact FDM used by Roul et al [13] for nonlinear singular BVPs with mixed boundary conditions has proved to be very effective in solving various physical models.…”

Section: Introductionmentioning

confidence: 99%

A High-Resolution Exponential Spline Method and Its Convergence Analysis for Two-Point Mixed Boundary Value Problems

Sharma,

Kaur

2024

Int. J. Comput. Methods

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In this paper, we present a new numerical method for effectively solving general second-order ordinary differential equations with mixed boundary conditions. Our approach utilizes a quasi-variable mesh enabling us the flexibility to adapt the mesh density according to different boundary layer problems. By employing a discretization technique that incorporates the construction of exponential spline, we achieve third-order accuracy at internal grid points, while boundary points exhibit fourth-order accuracy. Since the method is based on off-step grid points, it eliminates the need to modify the method while employing it to singular problems. We provide computational results to various numerical problems which arise in different physical phenomena like Burger’s equation and Sturm–Liouville equation. A comparison with recent findings underscores the superior performance of our method.

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High-precision numerical method for 1D quasilinear hyperbolic equations on a time-graded mesh: application to Telegraph model equation

2023

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High accuracy variable mesh method for nonlinear two-point boundary value problems in divergence form

Cited by 7 publications

References 19 publications

Hybrid Cubic B-Spline Method for Solving Non-Linear Two-Point Boundary Value Problems

Hybrid Cubic B-Spline Method for Solving Non-Linear Two-Point Boundary Value Problems

A High-Resolution Exponential Spline Method and Its Convergence Analysis for Two-Point Mixed Boundary Value Problems

High-precision numerical method for 1D quasilinear hyperbolic equations on a time-graded mesh: application to Telegraph model equation

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