How to schedule a batch class in the same batch class in Salesforce?

Hi,

We can write both batch and schedule in one class as both are interface we can implement more then one interface in one class which is basically known as multiple inheritance .
You can try like below-

global class BatchAndSchedule implements Schedulable,Database.Batchable<sObject>{
global Database.QueryLocator start(Database.BatchableContext BC){
String query = 'SELECT Id,Name FROM Account';
return Database.getQueryLocator(query);
}
global void execute(Database.BatchableContext BC, List<Account> scope){
for(Account acc : scope){
acc.Name = acc.Name +'ManojBatch';
}
update scope;
}
global void finish(Database.BatchableContext BC){ }
global void execute(SchedulableContext scon) {
Database.executeBatch(new BatchAndSchedule(),100);
}
}

Thanks.