Abstract

Banach space is a finished standard space, which implies that each Cauchy succession of the components of this space closes inside the actual space, and this is the thing that makes it a shut space It also has many applications in functional analysis. The aim of this paper is design and develop highly efficient algorithms that provide the existence of unique solutions to the differential equation in Banach spaces using MATLAB. The quality algorithm was used and developed to solve the differential equation in Banach spaces. For accurate results. The proposed model contributed to providing an integrated computer solution for all stages of the solution starting from the stage of solving differential equations in Banach space and the stage of displaying and representing the results graphically in the MATLAB program. This was done by solving three different types in type and rank to reach accurate readings that provide an ideal model applicable in many of the techniques that contribute to solving our daily problems. This study was distorted in the accuracy of the results with their comparisons from their platforms in the stages and type of solution, as the model achieved high accuracy in the presence of unique solutions to the differential equation in Banach spaces in a computerized form.

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References

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