scholarly journals The Direct Simulation of Third Order Linear Problems on Single Step Block Method

2021 ◽  
pp. 1-12
Author(s):  
J. Sabo ◽  
Y. Skwame ◽  
T. Y. Kyagya ◽  
J. A. Kwanamu
Keyword(s):  
Reduction Method ◽  
Direct Method ◽  
Numerical Test ◽  
Single Step ◽  
Test Problems ◽  
Direct Simulation ◽  
Block Method ◽  
Third Order ◽  
Order Linear ◽  
Linear Problems

In this article, the direct simulation of third order linear problems on single step block method has been proposed. In order to overcoming the setbacks in reduction method, direct method has been proposed using power series to reduce computational burden that occur in the reduction method. Numerical properties for the block method are established and the method developed is consistent, convergent and zero-stable. To validate the accuracy of the block method, certain numerical test problems were considered, the results shown that the accuracy of our method are more accurate over the existing method in literature.

scholarly journals On the Approximated Solution of a Special Type of Nonlinear Third-Order Matrix Ordinary Differential Problem

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2262
Author(s):  
Emilio Defez ◽  
Javier Ibáñez ◽  
José M. Alonso ◽  
Michael M. Tung ◽  
Teresa Real-Herráiz
Keyword(s):  
Differential Equations ◽  
Numerical Test ◽  
Test Problems ◽  
Science And Engineering ◽  
Third Order ◽  
Differential Problem ◽  
Order Matrix ◽  
Engineering Problems ◽  
Matrix Differential Equations ◽  
Matrix Differential

Matrix differential equations are at the heart of many science and engineering problems. In this paper, a procedure based on higher-order matrix splines is proposed to provide the approximated numerical solution of special nonlinear third-order matrix differential equations, having the form Y(3)(x)=f(x,Y(x)). Some numerical test problems are also included, whose solutions are computed by our method.

Some Further Results for a Reduction Method in Nonhierarchical Optimization-Based Design

1992 ◽  
Author(s):  
Bi-Chu Wu ◽  
Shapour Azarm
Keyword(s):  
Optimality Conditions ◽  
Reduction Method ◽  
Numerical Test ◽  
Verification And Validation ◽  
Previous Article ◽  
Test Problems ◽  
Engineering Systems ◽  
Test Results ◽  
Simple Reduction ◽  
Optimization Based Design

Abstract In a previous article, a new and simple reduction method was presented for optimization-based design of nonhierarchically decomposed engineering systems. As a sequel to that work, in this paper we first examine some significant issues in relation to the reduction method: the optimality conditions when the method is applied, the reason why move limits are not required, and some of the factors that might affect the robustness of the cumulative constraints. For verification and validation, we then present some numerical test results in which the method is applied to twenty-one (21) test problems. Based on the test results reported, some guidelines for applying the method are suggested.

scholarly journals Computational study of a 3-step hybrid integrators for third order ordinary differential equations with shift of three off-step points

2021 ◽  
pp. 459-468
Author(s):  
Mark I. Modebei ◽  
Olumide O. Olaiya ◽  
Ignatius P. Ngwongwo
Keyword(s):  
Differential Equations ◽  
Hybrid Method ◽  
Computational Analysis ◽  
Computational Study ◽  
Single Step ◽  
Stability And Convergence ◽  
Test Problems ◽  
Third Order ◽  
Cpu Time ◽  
Direct Approximation

A Block of hybrid method with three off-step points based is presented in this work for direct approximation of solution of third-order Initial and Boundary Value Problems (IVPs and BVPs). This off-step points are formulated such that they exist only on a single step at a time. Hence, these points are shifted to three positions respectively in order to obtain three different integrators for computational analysis. These analysis includes; order of the methods, consistency, stability and convergence, global error, number of functions evaluation and CPU time. The superiority of these methods over existing methods is established numerically on different test problems in literature

Chemical equilibrium systems as numerical test problems

1990 ◽  
Vol 16 (2) ◽  
pp. 143-151 ◽  
Author(s):  
Keith Meintjes ◽  
Alexander P. Morgan
Keyword(s):  
Chemical Equilibrium ◽  
Numerical Test ◽  
Test Problems

scholarly journals On non-homogeneous canonical third-order linear differential equations

1994 ◽  
Vol 57 (2) ◽  
pp. 138-148 ◽  
Author(s):  
N. Parhi
Keyword(s):  
Differential Equations ◽  
Linear Equations ◽  
Sufficient Conditions ◽  
Linear Differential Equations ◽  
Third Order ◽  
Order Linear ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

AbstractIn this paper sufficient conditions have been obtained for non-oscillation of non-homogeneous canonical linear differential equations of third order. Some of these results have been extended to non-linear equations.

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