A New Special 15-Step Block Method for Solving General Fourth Order Ordinary Differential Equations
Victor Oboni Atabo, Solomon O. Adee
Abstract
A new higher-implicit block method for the direct numerical solution of fourth order ordinary differential equation is derived in this research paper. The formulation of the new formula which is 15-step, is achieved through interpolation and collocation techniques. The basic numerical properties of the method such as zero-stability, consistency and A-stability have been examined. Investigation showed that the new method is zero stable, consistent and A-stable, hence convergent. Test examples from recent literature have been used to confirm the accuracy of the new method.
Topics & Concepts
Ordinary differential equationMathematicsCollocation (remote sensing)Collocation methodNumerical methods for ordinary differential equationsLinear multistep methodInterpolation (computer graphics)Stability (learning theory)Applied mathematicsBlock (permutation group theory)Consistency (knowledge bases)Explicit and implicit methodsNumerical stabilityMathematical analysisNumerical analysisDifferential equationComputer scienceDifferential algebraic equationGeometryMachine learningComputer graphics (images)AnimationNumerical methods for differential equationsElectromagnetic Simulation and Numerical MethodsMatrix Theory and Algorithms